Probability and complex function: Unit V: Ordinary Differential Equations

Method of variation of parameters

Ordinary Differential Equations

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This method is very useful in finding the general solution of the second order equation

METHOD OF VARIATION OF PARAMETERS.

This method is very useful in finding the general solution of the second order equation

d2y/dx2 + a1dy/dx+a2 y = X [where 'X' is a function of x]... (1)

The complementary function of (1)

C.F = C1f1 + C2f2 .......(2)

where C1, C2 are constants and f1 and f2 are functions of x.

Then,

P.I = P f1 + Q f2  ............(3)


y= C1f1+ C2f2 + P.I

Note: The Wronskian of f1, f2 of (1) is given by


Probability and complex function: Unit V: Ordinary Differential Equations : Tag: : Ordinary Differential Equations - Method of variation of parameters

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Probability and complex function: Unit V: Ordinary Differential Equations


Ordinary Differential Equations - Introduction

Higher order linear differential equations with constant coefficients

(a) Problems based on r.h.s. of the given differential equation is zero - Solved Example Problems | Ordinary Differential Equations

(b) Problems based on P.I.= 1/f(D) eax ⇒ Replace D by a - Solved Example Problems | Ordinary Differential Equations

(c) Problems based on P.I = 1 / f(D) sin ax or 1 / f(D) cos ax ⇒ Replace D2 by -a2 - Solved Example Problems | Ordinary Differential Equations

(d) problems based on R.H.S = eax + sin ax(or) eax + cos ax - Solved Example Problems | Ordinary Differential Equations

(e) problems based on R.H.S = xn - Solved Example Problems | Ordinary Differential Equations

(f) Problems based on R.H.S. = eax X - Solved Example Problems | Ordinary Differential Equations

(g) problems based on f(x) = x V type - Solved Example Problems | Ordinary Differential Equations

(h) problems based on eax integral e-ax - Solved Example Problems | Ordinary Differential Equations

(i) General ode problems - Solved Example Problems | Ordinary Differential Equations

(i) Problems based on R.H.S = eax + xn + cos ax - Solved Example Problems | Ordinary Differential Equations

Exercise 5.1 (Ordinary Differential Equations) - Problems with Answer

Method of variation of parameters - Ordinary Differential Equations

Problems based on method of variation of parameters - Solved Example Problems | Ordinary Differential Equations

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