## anonymous 4 years ago Can someone help me to solve this differential eqation please. y''+9y=cosx (i got solution to homogeneuos equation: c1*cos(3x)+c2*sin(3x) ) i have tried to find particular with variation of parameters, with wronskian...i have so weird integral :(

1. anonymous

try going to wolframalpha.com

2. lalaly

have u tried undetermined coeffecients?

3. lalaly

$y_p=Acosx + Bsinx$$y_p'=-Asinx+Bcosx$$y_p''=-Acosx-Bsinx$substitute in equation $-Acosx-Bsinx+9(Acosx+Bsinx)=cosx$$-Acosx-Bsinx+9Acosx +9Bsinx=cosx$$8Acosx+8Bsinx=cosx$$8A=1$$A=\frac{1}{8}$$8B=0$$B=0$ so $y_p=\frac{1}{8}cosx$$y=y_h + y_p$$=c_1\cos3x+c_2\sin3x +\frac{1}{8}cosx$