Differential Equations (ODE)

First-Order ODEs

1. Separable & Exact Equationssolution methods, integrating factors, existence and uniqueness3–6 h
2. Linear First-Order ODEsintegrating factor, Bernoulli equation3–6 h
3. Applications of First-Order ODEsmixing, cooling, population, radioactive decay, circuits3–6 h

Second-Order & Systems

1. Second-Order Linear Equationshomogeneous with constant coefficients, reduction of order3–6 h
2. Nonhomogeneous Equationsundetermined coefficients, variation of parameters, resonance3–6 h
3. Series Solutionsordinary vs singular points, Frobenius method3–6 h
4. Systems of ODEseigenvalue method, phase portraits, matrix exponentials3–6 h

Transform & Qualitative Methods

1. Laplace Transformstransforms, inverse, convolution, solving IVPs, transfer functions3–6 h
2. Stability & Phase Planeequilibrium classification, linearization, Lyapunov stability3–6 h
3. Numerical MethodsEuler, Runge-Kutta, error analysis3–6 h
4. ODE Applicationsspring-mass, pendulum, coupled oscillators, control systems3–6 h