Need solve a differential equations with laplace transforms: y′′−y′−2y=4x^2,y(0)=−1,y′(0)=1

zakownikbj

zakownikbj

Answered question

2022-09-23

Need solve a differential equations with laplace transforms:
y y 2 y = 4 x 2 , y ( 0 ) = 1 , y ( 0 ) = 1
And I'm having trouble specifically because of the forcing part, 4 x 2 , which causes me to have two variables in the transformed equation Y(s).
Y ( s ) = s + ( 8 / r 3 ) s 2 s 2
Is this correct, and then how do I get Y(s) into a form that I can take the inverse laplace of?

Answer & Explanation

Zariah Fletcher

Zariah Fletcher

Beginner2022-09-24Added 8 answers

It should be 8 / s 3 . You either use r or s as a variable. If you are using s as the variable for Laplace transform, you have L [ f ( x ) ] = 0 f ( x ) e s t d t, so that L [ 4 x 2 ] = 8 / s 3

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