Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = x² + y², y(0) = 3; y(0.5) (h = 0.1) (h= 0.05) y(0.5) y(0.5)

Please solve the following, provide well explained and readable solution.

Solve the initial value problem below using the method of Laplace transforms. 5t y" - 6y' + 25y = 20 e ", y(0) = 1, y'(0) = 9 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) = (Type an exact answer in terms of e.)