Answer to Question #198298 in Differential Equations for muhammad Ahmad

Question #198298

Three students were given a differential equation y''+π ^2y=0 to solve. 


1
Expert's answer
2021-05-26T03:16:35-0400

y+π2y=0y''+\pi^2y=0

d2ydx2=y=D2y\dfrac{d^2y}{dx^2}=y''=D^2y

D2y+π2y=0D^2y+\pi^2y=0

(D2+π2)y=0(D^2+\pi^2)y=0


Auxiliary equation,

D2+π2=0D^2+\pi^2=0

D2=π2D^2=-\pi^2

D=±iπD=\pm i\pi


Complimentary function is given by,

y=C1eiπ+C2eiπy=C_1e^{i\pi}+C_2e^{-i\pi}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment