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(Higher order riation of parameter) Consi- 12 &(n) + Cª(z)g(0) = g(n). as(x) y(i) = g(n) + an-1(x)y ssume that y₁,,n are n-independent solutio- on. Prove that a particular integral of the give

(Higher order riation of parameter) Consi- 12 &(n) + Cª(z)g(0) = g(n). as(x) y(i) = g(n) + an-1(x)y ssume that y₁,,n are n-independent solutio- on. Prove that a particular integral of the give

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(Higher order riation of parameter) Consider the n-th order linear equation g(n) + -Σªs(2)y(¹) = g(n) + ªn-1(2)g(0-¹) + - - - + ao(z)y = r(s). ... Assume that y₁,, are n-independent solutions of the associated homogeneous equa- tion. Prove that a particular integral of the given ODE is Up = [v., where = u R₁ Here W is the wronskian of y₁,...,n and R is the determinant obtained by replacing i-th column of W by [0,0,...,0, (x)].
Transcribed Image Text:(Higher order riation of parameter) Consider the n-th order linear equation g(n) + -Σªs(2)y(¹) = g(n) + ªn-1(2)g(0-¹) + - - - + ao(z)y = r(s). ... Assume that y₁,, are n-independent solutions of the associated homogeneous equa- tion. Prove that a particular integral of the given ODE is Up = [v., where = u R₁ Here W is the wronskian of y₁,...,n and R is the determinant obtained by replacing i-th column of W by [0,0,...,0, (x)].
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