Solution Set Differential Equation & Laplace Transform

SYLLABUS- Sol. Set: DIFFERENTIAL EQUATION & LAPLACE TRANSFORM, 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.