Course Syllabus:
UNIT – I (12 Hours)
Differential Equations of first order and first degree:
Linear Differential Equations; Differential equations reducible to linear form; Exact differential
equations; Integrating factors; Change of variables
UNIT – II (12 Hours)
Orthogonal Trajectories
Differential Equations of first order but not of the first degree:
Equations solvable for p; Equations solvable for y; Equations solvable for x; Equations that do not
contain x (or y); Equations homogeneous in x and y;Equations of the first degree in x and y – Clairaut’s
Equation.
UNIT – III (12 Hours)
Higher order linear differential equations-I:
Solution of homogeneous linear differential equations of order n with constant coefficients; Solution of
the non-homogeneous linear differential equations with constant coefficients by means of polynomial
operators.General Solution of f(D)y=0.
General Solution of f(D)y=Q when Q is a function of x,
1
f D
is expressed as partial fractions.
P.I. of f(D)y = Q when Q=
ax be
P.I. of f(D)y = Q when Q is bsinax or b cos ax
UNIT – III (12 Hours)
Higher order linear differential equations-I:
Solution of homogeneous linear differential equations of order n with constant coefficients; Solution of
the non-homogeneous linear differential equations with constant coefficients by means of polynomial
operators.General Solution of f(D)y=0.
General Solution of f(D)y=Q when Q is a function of x,
1
f D
is expressed as partial fractions.
P.I. of f(D)y = Q when Q=
ax be
P.I. of f(D)y = Q when Q is bsinax or b cos ax.
UNIT –V (12 Hours)
Higher order linear differential equations-III :
Method of variation of parameters; Linear differential Equations with non-constant coefficients; The
Cauchy-Euler Equation, Legendre's linear equations, miscellaneous differential equations.
