Differential Equations Notes for Gate 2026

Differential equations form the core of mathematical modeling in science and engineering. They describe how quantities change and help us understand real-world systems like electrical circuits, heat flow, population growth, and mechanical vibrations. By relating functions with their derivatives, differential equations provide powerful tools to predict behavior, analyze stability, and solve complex engineering problems. For GATE and competitive exams, mastering differential equations strengthens both conceptual understanding and problem-solving accuracy.

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Differential Equation Notes for Gate 2026

The following topics are discussed in differential equation, 

1. Differential Equation 
2. Order of Differential Equation
3. Degree of Differential Equation
4. Homogeneous Differential Equation 
5. Linear Differential Equation

First Order Equations:

• Variable Separable Method
• Equations Reduced to Variable Separable Method
• Homogeneous D.E
• Exact D.E
• Non-Exact D.E
• Linear D.E
• Bernoulli's D.E
• Non-Linear D.E

In Non-Exact, Types of Integrating Factor:

• Type-1
• Type-2
• Type-3
• Type-4

Higher Order Differential Equation:

      Particular Integral:

• Type- 1 P.I
• Type- 2 P.I
• Type- 3 P.I
• Type- 4 P.I

Part-II

1. Methods of Variation of Parameters
2. Cauchy Euler Equation
3. Partial Differential Equations
4. Classification of Second-Order Linear Partial Differential Equations.
5. Lagrange's Linear Partial D.E
6. Non-linear Partial Differential Equations

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Conclusion

Differential equations form the backbone of engineering mathematics, and mastering them is essential for securing a strong score in GATE 2026. These notes are designed to simplify concepts, provide step-by-step methods, and build the analytical thinking required to tackle both theoretical and numerical questions. With structured explanations, solved examples, and practice problems, you will develop the confidence to solve even the most challenging differential equation problems quickly and accurately.

Consistent revision along with these notes will help you strengthen fundamentals, improve problem-solving speed, and approach the exam with clarity and precision. Stay focused, keep practicing, and let these notes guide you towards your GATE success.