Differential equations Topics - GATE ME Syllabus

1

Solution methods for first-order ODEs.

1m3/10

📌 Key FormulaIntegrating factor for linear

2

Characteristic equation method for linear homogeneous/non-homogeneous.

1m4/10

📌 Key FormulaAuxiliary equation roots

3

Equidimensional equations solved by assumed power solution.

1m4/10

📌 Key Formulax^m assumption

4

Applying conditions to find unique solutions.

1m3/10

📌 Key Formulay(0), y'(0) etc.

5

Transform method for solving ODEs with initial conditions.

1m4/10

📌 Key FormulaL{f(t)} = ∫ e^{-st} f(t) dt

6

PDE solutions for heat conduction problems.

1m4/10

📌 Key FormulaSeparation of variables

7

Wave equation solutions for vibrations.

1m4/10

📌 Key Formulad'Alembert or separation

8

Steady-state potential problems (∇²φ=0).

1m4/10

📌 Key FormulaLaplace equation