Using the method of variation of parameters, solve the following inhomogeneous equation. y′′+12y′+36y=(−1e−6x)/(x2+1) a) Write the characteristic equation of the homogeneous part of the equation using the variable m. ....?....=0 b) Write down the homogeneous solution of the equation. Denote the constants c1 and c2 with c1 and c2. The y1 and y2 solutions must satisfy the conditions y1(0)=1, y2(0)=0, respectively. yh=? c) Find Wronskian: W(y1,y2)=?
Using the method of variation of parameters, solve the following inhomogeneous equation. y′′+12y′+36y=(−1e−6x)/(x2+1) a) Write the characteristic equation of the homogeneous part of the equation using the variable m. ....?....=0 b) Write down the homogeneous solution of the equation. Denote the constants c1 and c2 with c1 and c2. The y1 and y2 solutions must satisfy the conditions y1(0)=1, y2(0)=0, respectively. yh=? c) Find Wronskian: W(y1,y2)=?
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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Using the method of variation of parameters, solve the following inhomogeneous equation.
y′′+12y′+36y=(−1e−6x)/(x2+1)
a) Write the characteristic equation of the homogeneous part of the equation using the variable m.
....?....=0
b) Write down the homogeneous solution of the equation. Denote the constants c1 and c2 with c1 and c2. The y1 and y2 solutions must satisfy the conditions y1(0)=1, y2(0)=0, respectively.
yh=?
c) Find Wronskian: W(y1,y2)=?
d) W1=?
e) W2=?
f) u′1=? u1=?
g)u′2=? u2=?
h) Write down the specific solution you got: yp=?
e) Write down the general solution of the equation: y=?
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