Differential Equations

Formulas are organized based on their importance in the CAT exam.
1 Determining the Remaining Function
2 Integrating Factor
3 Differential Equation from a Family of Curves
4 Mean Life
5 Angular Frequency of Spring-Mass SHM
6 Differential Equation of a Straight-Line Family
7 Differential Equation of Parallel Lines
8 Differential Equation for a Spring-Mass System
9 Time Period of Spring-Mass SHM
10 Degree of a Differential Equation
11 Explicit Linear Solution
12 Differential Equation of a Circle with Variable Radius
13 Differential Equation of Lines Passing Through a Fixed Point
14 Differential Equation of a Family of Curves
15 Initial Condition
16 Applying an Initial Condition
17 General Solution of a Separable Equation with Initial Condition
18 Differential Equation for Exponential Growth
19 Variation of Parameters (Particular Integral)
20 Formation by Eliminating Arbitrary Constants
21 Clairaut's Form
22 Tangent Equation
23 Exponential Growth/Decay with Initial Condition
24 Exact Differential Equation Test
25 Second Order Linear Homogeneous DE (Constant Coefficients)
26 Linear Differential Equation (First Order)
27 Exponential Growth/Decay Between Two Points
28 Exact Differential Equation
29 Second Order Linear Non-Homogeneous DE
30 Exponential Growth Model
31 Exponential Decay Equation
32 Solution of Exponential Growth Equation
33 First-Order Decay Toward Zero
34 Order of a Differential Equation
35 Slope of a Solution Curve
36 Solution of a Linear Differential Equation
37 Differential Equation for a Simple Pendulum
38 Logistic Differential Equation
39 Time Period of a Simple Pendulum
40 Orthogonal Trajectories
41 Exponential Decay Model
42 Family of Lines with Fixed Slope
43 Angular Frequency of a Simple Pendulum
44 Time Required for Motion
45 Percentage Remaining in Exponential Decay
46 Variable Separation in Logistic Equation
47 Partial Fraction for Logistic Equation
48 Constant Solution
49 Velocity from Position-Dependent Acceleration
50 Growth Model with Initial Value
51 Energy Form of Motion Equation
52 Autonomous Differential Equation
53 Work-Energy Differential Relation
54 Differential Equation of the Form
55 Rate Proportional to Difference
56 First-Order Differential Equation
57 Solution of an Exact Differential Equation
58 Bernoulli's Equation
59 Particular Solution from Initial Condition
60 Autonomous Equation by Separation
61 Differential Equation from a Given Solution
62 Solution for Falling Body with Linear Resistance
63 Kinetic Energy from Differential Equation
64 Terminal Velocity as a Limiting Value
65 Differential Equation for Mixing Problems
66 Bernoulli Equation with Reciprocal Variable
67 Formation by Differentiation
68 Exact Equation Potential Function
69 Decay Model with Initial Value
70 Relation Between First and Second Derivatives
71 Position of a Falling Body with Linear Resistance
72 Constant-Volume Mixing
73 Separable Equation with Initial Condition
74 Rate of Solute Leaving
75 Mixing Differential Equation
76 Linear Differential Equation in Differential Form
77 Integrating Factor Transformation
78 Exponential Decay Equation
79 Newton's Law of Cooling in Differential Form
80 SHM Acceleration
81 Standard Logistic Solution
82 Exact Differential Equation
83 First-Order Differential Equation for Motion
84 Orthogonal Trajectories
85 Bernoulli Equation for Reciprocal Power
86 Differential Equation of Circles Centered at Origin
87 Separated Homogeneous Equation
88 Condition for Parallel Linear Expressions
89 Differential Equation Reducible to Homogeneous Form
90 Rate of Solute Entering
91 Concentration
92 Logarithmic Form of Logistic Solution
93 Continuous Growth with Variable Rate
94 Linear Differential Equation Solution
95 Differential Equation for Motion with Position-Dependent Acceleration
96 Equilibrium Solution
97 Finding Potential Function from M
98 Linear Equation in Differential Form
99 Linear Equation with Zero Right-Hand Side
100 Solution of Variable-Rate Growth
101 Differential Equation for Simple Harmonic Motion
102 Logistic Solution with Initial Value
103 Variable Separable Form
104 Family of Circles Centered on the x-Axis
105 Alternative Homogeneous Substitution
106 Method of Undetermined Coefficients (Particular Integral)
107 Determining the Missing Function
108 Solution Through a Given Point
109 Translation of Variables
110 Logistic Differential Equation
111 Differential Equation of Parallel Lines
112 Direct Variable Separation
113 Linear Equation with Constant Coefficients
114 Newton's Law of Cooling Between Two Measurements
115 Formation with Two Arbitrary Constants
116 General Solution of a Differential Equation
117 Bernoulli Differential Equation
118 Solution of a Separable Differential Equation
119 Variable Separable Differential Equation
120 Family of Lines Through a Fixed Point
121 Differential Equation for Cooling
122 Newton's Law of Cooling Solution
123 Derivative of the Integrating Factor
124 Rate of Change of Temperature
125 Linear Equation with Constant Coefficients and Zero RHS
126 Formation of Differential Equation
127 Bernoulli Substitution
128 Normal Equation from Differential Equation
129 Differential Equation of Exponential Family
130 Differential Equation of the Form
131 First Integral
132 Terminal Velocity with Linear Resistance
133 Relation Between Mean Life and Half-Life
134 Verifying a Solution
135 Homogeneous Differential Equation
136 Bernoulli Equation After Substitution
137 Acceleration as a Function of Position
138 Linear Equation with Constant Coefficients
139 General Trigonometric Differential Equation
140 Linear Equation with Constant Coefficients and Zero RHS
141 Integrating Factor for Non-Exact Equation
142 Linear Differential Equation for x as a Function of y
143 Integrating Factor Depending Only on y
144 Initial-Value Problem
145 Linear Equation After Multiplication by IF
146 Time from Cooling Equation
147 Family of Circles Passing Through the Origin
148 Differential Equation of Sinusoidal Family
149 Continuous Decay with Variable Rate
150 Orthogonal Trajectory Method
151 Solution for x as a Function of y
152 First-Order Equation for a Falling Body with Linear Resistance
153 Exponential Model from Two Values
154 Variable Transformation for $$x=vy$$
155 Integrating Factor Depending Only on x
156 Differential Equation of a Family of Circles
157 Differential Equation for Constant nth Derivative
158 Normal Equation
159 Orthogonal Trajectory Differential Equation
160 Doubling Time
161 Variable Transformation
162 Half-Life
163 Linear Differential Equation
164 Maximum Growth Rate
165 Differential Equation for Radioactive Decay
166 Separable Equation with Constant Factor
167 SHM Velocity
168 Homogeneous Substitution
169 Activity
170 Activity as a Function of Time
171 Particular Solution
172 Differential Equation of a Family of Curves
173 General Solution of Linear Equation
174 Linear Homogeneous Equation
175 Cooling Model with Initial Temperature
176 Differential Equation for Constant Rate
177 Differential Equation of a Family of Parabolas
178 Homogeneous Differential Equation
179 Limiting Value
180 Normal Slope
181 Bernoulli Substitution
182 Bernoulli Equation After Substitution
183 Rate of Change of a Quantity
184 Half-Life and Decay Constant
185 Differential Equation
186 Differential Equation of Circles with Centre on x-Axis
187 Degree of a Differential Equation
188 Tangent Equation from Differential Equation
189 Differential Equation of Power Family
190 Separable Solution
191 Finding Potential Function from N
192 Orthogonality in Differential Form
193 Homogeneous Solution After Integration
194 Bernoulli Differential Equation
195 Differential Equation of Power Curves
196 Linear Differential Equation
197 Logarithmic Differentiation in Differential Equations
198 Product Derivative Used in Linear Equations
199 First-Order Approach to Equilibrium
200 Solution of Newton's Cooling Equation
201 Radioactive Decay Law
202 Maximum Logistic Growth Rate
203 Differential Equation of Logarithmic Family
204 Differential Equation for Compound Growth
205 Differential Equation of a Family of Exponential Curves
206 Carrying Capacity
207 Differential Equation of a Curve with Known Slope
208 Separated Form After Homogeneous Substitution
209 General Solution
210 Differential Equation as a Family of Curves
211 Separable Equation with Reciprocal Function
212 Bernoulli Equation with Negative Power
213 Differential Form of a Separable Equation
214 Homogeneous Equation in $$x/y$$
215 Differential Equation for Constant Second Derivative
216 Product-Derivative Form
217 Logistic Solution
218 Order of a Differential Equation
219 Differential Equation of a Parabola Family
220 Separable Form After Homogeneous Substitution
221 Growth/Decay Constant
222 Homogeneous Substitution
223 Potential Function for Exact Equation
224 Exact Differential Equation
225 Orthogonal Trajectories
226 Finding the Potential Function
227 Separable Equation
228 Exponential Growth Equation
229 Standard SHM Solution
230 Homogeneous Differential Equation
231 Formation with n Arbitrary Constants
232 Integrating Factor
233 Differential Equation of a Straight-Line Family
234 Tangent Slope from a Differential Equation
235 Cauchy-Euler Equation