Laplace transform solve integral equation

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Homework Statement



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Homework Equations


The Attempt at a Solution



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The answer is y(t) = [itex]t^{4}+\frac{t^{6}}{30}[/itex]

Don't know what to do next any advices please
 
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lurflurf said:
solve algebraically for L{y}

L{y}=L{t^4}+L{y}L{sin(t)}

u meant put L{y} to the same side and then reverse transform? I'm try that way but still didnt get that answer
 
lurflurf said:
solve algebraically for L{y}

L{y}=L{t^4}+L{y}L{sin(t)}

Thanks lurflurf I got it now :)