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Description of  TB Differential Equations & Laplace Transforms , Edition-3

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.