Question: y''+y = sinx ; y(0)=0, y'(0)=2 Solve using IVP using LaPlace Tranfer S 2 L{y(s)} - s y(0) - y'(0) + L{y(s)} = 1/s 2

y''+y = sinx ; y(0)=0, y'(0)=2

Solve using IVP using LaPlace Tranfer

S2 L{y(s)} - s y(0) - y'(0) + L{y(s)} = 1/s2 +1

[S2+1 ] -2 + L{y(s)} = 1/s2+1

[s2+1] L{y(s)} = 1+2(s2+1)/s2+1

L{y(s)} = 2s2+3 / (s2+1)2

this is where I'm lost I've tried several different ways but no luck.

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