Differential Equations & Laplace Transforms

SYLLABUS- DIFFERENTIAL EQUATIONS & LAPLACE TRANSFORMS, Section A
Differential Equations: Differential Equations of first order higher degree, Differential equations solvable for p, y and x. Differential Equation of Clairaut’s form, Differential Equations reducible to Clairaut’s form, Singular solutions. Geometrical meaning of a differential equation of first order, Differential equation of
orthogonal trajectories, Linear differential equations with constant coefficients. Homogeneous linear differential equations, Differential equations reducible to the homogeneous linear form, Simultaneous differential equations.
Section B
Linear differential equations of second order with variable coefficients,
Transformations of differential equations by changing the depended and
independent variables. Method of variation of parameters. Total differential
equations.
Laplace Transform: Existence theorem for Laplace transforms. Properties of
Laplace transforms, Laplace transforms of derivatives and integrals, Laplace
transforms of unit step and Dirac Delta functions, Inverse Laplace transform,
Properties of Inverse Laplace transforms, Inverse Laplace transforms of derivatives
and integrals, Convolution Theorem, Solutions of ordinary differential equations
using Laplace transform, Solutions of simultaneous differential equations using
Laplace transform.