Ordinary Differential Equations: Equations of First Order and of Degree Higher than one
– Solvable for p, x, y – Clairaut’s Equation – Simultaneous Differential Equations with constant
coefficients of the form
i) f1(D)x + g1(D)y = ( ) 1 f t
ii) f2(D)x + g2(D)y = ( ) 2 f t
where f1 , g1 , f2 and g2 are rational functions
D = with constant coefficients 1
f and 2 f explicit
functions of t.
Finding the solution of Second and Higher Order with constant coefficients with Right
Hand Side is of the form Veax where V is a function of x – Euler’s Homogeneous Linear
Differential Equations – Method of variation of parameters.
Anx.18 D - B.Sc Maths (SDE) 2007-08 Page 6 of 26
Partial Differential Equations: Formation of equations by eliminating arbitrary constants
and arbitary functions – Solutions of P.D Equations – Solutions of Partial Differential Equations
by direct integration – Methods to solve the first order P.D. Equations in the standard forms -
Lagrange’s Linear Equations.
Laplace Transforms: Definition – Laplace Transforms of standard functions – Linearity
property – Firsting Shifting Theorem – Transform of tf(t), ( )
, f1(t), f11(t).
Inverse Laplace Transforms – Applications to solutions of First Order and Second Order
Differential Equations with constant coefficients.