Solve the differential equations by using Laplace transforms:(d^(2)t)/(dt^(2))+(dx) / (dt)-6x=1, at t=0, x=0, dx/dt=1

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

Please solve this Using Mathematica and upload the (.nb) file

(a) Solve the differential equation:

Plot multiple solutions of the differential equation with values of constants c -2,-1,0,1,2 in a single graph

(b)   

Find the value of y(4)

(c) Plot the numerical solution of the differential equation for 0 ≤ χ  ≤ 10:

dy 2 Secar 4.b) Solve the differential equation + - y = -2 [5 marks]