Class 12 Math: Differential Equations Quick Revision Chapter Summary

Need to review the entire chapter before a test? This quick revision guide summarizes all the core concepts, topics, and equations taught in Class 12 Differential Equations to help you refresh your memory instantly.

Core Topics At a Glance

### 📌 Definition, order, and degree A differential equation is an equation involving an unknown function and its derivatives. Order is the highest derivative present. Degree is the power of the highest order derivative, provided the equation is a polynomial in derivatives.

### 📌 General and particular solutions of differential equations The general solution of an n-th order differential equation contains n arbitrary constants. A particular solution is obtained by assigning specific values to these constants using initial or boundary conditions.

### 📌 Separable variable differential equations Separable differential equations can be solved by grouping all terms in 'y' on one side with dy, and all terms in 'x' on the other side with dx, and integrating both sides independently.

### 📌 Homogeneous differential equations A differential equation is homogeneous if it can be written as dy/dx = F(y/x). It is solved by substituting y = vx, which transforms it into a separable equation in v and x.

### 📌 Linear differential equations first order A first-order linear differential equation is of the form dy/dx + Py = Q, where P and Q are functions of x. It is solved by multiplying the equation by an Integrating Factor (IF) to make it integrable.

Key Formulas Mind Map

• Linear Differential Equation: `\frac{dy}{dx} + P y = Q` - Standard form where P and Q are functions of x....
• Integrating Factor: `IF = e^{\int P \, dx}` - Multiplying factor to solve linear differential equations....

Revision Checklist

1. Review the subtopic guides and outline notes.
2. Practice writing the key formulas from memory.
3. Solve at least 3 worked examples and check your steps.
4. Take a timed practice quiz to verify your speed.