Differential Equations

Formulas are organized based on their importance in the CAT exam.
1 Determining the Remaining Function
2 Differential Equation from a Family of Curves
3 Angular Frequency of Spring-Mass SHM
4 Differential Equation of a Straight-Line Family
5 Mean Life
6 Slope of a Solution Curve
7 Linear Differential Equation Solution
8 Differential Equation of Parallel Lines
9 General Solution of a Separable Equation with Initial Condition
10 Exponential Growth/Decay with Initial Condition
11 Relation Between Mean Life and Half-Life
12 Time Period of Spring-Mass SHM
13 Linear Equation with Zero Right-Hand Side
14 Variable Separable Differential Equation
15 Explicit Linear Solution
16 Differential Equation of a Circle with Variable Radius
17 Differential Equation of Lines Passing Through a Fixed Point
18 Linear Equation in Differential Form
19 Degree of a Differential Equation
20 Solution of Variable-Rate Growth
21 Integrating Factor
22 Differential Equation of a Family of Curves
23 Logistic Differential Equation
24 Initial Condition
25 Formation by Eliminating Arbitrary Constants
26 Variable Separation in Logistic Equation
27 Energy Form of Motion Equation
28 Translation of Variables
29 Clairaut's Form
30 Differential Equation for Exponential Growth
31 Differential Equation for a Spring-Mass System
32 Tangent Equation
33 Exponential Growth/Decay Between Two Points
34 Linear Differential Equation (First Order)
35 Second Order Linear Homogeneous DE (Constant Coefficients)
36 Applying an Initial Condition
37 Exact Differential Equation Test
38 Second Order Linear Non-Homogeneous DE
39 Exact Differential Equation
40 First-Order Decay Toward Zero
41 Exponential Growth Model
42 Exponential Decay Equation
43 Solution of a Linear Differential Equation
44 Order of a Differential Equation
45 Time Period of a Simple Pendulum
46 Differential Equation for a Simple Pendulum
47 Exponential Decay Model
48 Family of Lines with Fixed Slope
49 Angular Frequency of a Simple Pendulum
50 Time Required for Motion
51 Orthogonal Trajectories
52 Percentage Remaining in Exponential Decay
53 Partial Fraction for Logistic Equation
54 Constant Solution
55 Velocity from Position-Dependent Acceleration
56 Variation of Parameters (Particular Integral)
57 Solution of Exponential Growth Equation
58 Growth Model with Initial Value
59 Work-Energy Differential Relation
60 Differential Equation of the Form
61 Rate Proportional to Difference
62 Autonomous Differential Equation
63 Solution of an Exact Differential Equation
64 First-Order Differential Equation
65 Bernoulli's Equation
66 Particular Solution from Initial Condition
67 Differential Equation from a Given Solution
68 Solution for Falling Body with Linear Resistance
69 Kinetic Energy from Differential Equation
70 Terminal Velocity as a Limiting Value
71 Differential Equation for Mixing Problems
72 Bernoulli Equation with Reciprocal Variable
73 Exact Equation Potential Function
74 Autonomous Equation by Separation
75 Constant-Volume Mixing
76 Separable Equation with Initial Condition
77 Formation by Differentiation
78 Decay Model with Initial Value
79 Relation Between First and Second Derivatives
80 Position of a Falling Body with Linear Resistance
81 Linear Differential Equation in Differential Form
82 Rate of Solute Leaving
83 Mixing Differential Equation
84 Integrating Factor Transformation
85 Exponential Decay Equation
86 Newton's Law of Cooling in Differential Form
87 SHM Acceleration
88 Standard Logistic Solution
89 First-Order Differential Equation for Motion
90 Orthogonal Trajectories
91 Bernoulli Equation for Reciprocal Power
92 Differential Equation of Circles Centered at Origin
93 Exact Differential Equation
94 Separated Homogeneous Equation
95 Condition for Parallel Linear Expressions
96 Differential Equation Reducible to Homogeneous Form
97 Logarithmic Form of Logistic Solution
98 Concentration
99 Rate of Solute Entering
100 Continuous Growth with Variable Rate
101 Differential Equation for Motion with Position-Dependent Acceleration
102 Equilibrium Solution
103 Finding Potential Function from M
104 Logistic Solution with Initial Value
105 Variable Separable Form
106 Alternative Homogeneous Substitution
107 Method of Undetermined Coefficients (Particular Integral)
108 Solution Through a Given Point
109 Logistic Differential Equation
110 Differential Equation of Parallel Lines
111 Direct Variable Separation
112 Linear Equation with Constant Coefficients
113 Newton's Law of Cooling Between Two Measurements
114 Formation with Two Arbitrary Constants
115 Family of Circles Centered on the x-Axis
116 Bernoulli Differential Equation
117 Newton's Law of Cooling Solution
118 Derivative of the Integrating Factor
119 Rate of Change of Temperature
120 Formation of Differential Equation
121 Bernoulli Substitution
122 Linear Equation with Constant Coefficients and Zero RHS
123 Normal Equation from Differential Equation
124 Differential Equation of Exponential Family
125 Differential Equation for Simple Harmonic Motion
126 General Solution of a Differential Equation
127 Determining the Missing Function
128 Solution of a Separable Differential Equation
129 Family of Lines Through a Fixed Point
130 Differential Equation for Cooling
131 Differential Equation of the Form
132 First Integral
133 Verifying a Solution
134 Terminal Velocity with Linear Resistance
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