# solve (x^2y"-xy'+y=(x^2+1) using laplace transformsPlease show all your work, and do not use eulers technique once the first Laplace transform has been applied, as that is not what I am curious about. However if it is not possible to solve this particular ODE using only Laplace transforms in combination with other ODE solving techniques (once the Laplace transform has been applied). Then please let me know

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solve (x^2y"-xy'+y=(x^2+1) using laplace transforms
Please show all your work, and do not use eulers technique once the first Laplace transform has been applied, as that is not what I am curious about. However if it is not possible to solve this particular ODE using only Laplace transforms in combination with other ODE solving techniques (once the Laplace transform has been applied). Then please let me know

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Step 1

This is an exercise in solving differential equations by using Laplace transforms (and its properties).

Step 2

Note that the given differential equation has non-constant coefficients. Let us try to apply Laplace transform and look at the modified equation for Y'(s) = (Laplace transform of y(t))

Step 3

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