What is the solution for 2y^{''}-7y^'+5y=11-7x-16x^2+5x^3 ?

The solution for 2y^{''}-7y^'+5y=11-7x-16x^2+5x^3 is y=c_{1}e^{(5x)/2}+c_{2}e^x+x^3+x^2-x

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2y^{''}-7y^'+5y=11-7x-16x^2+5x^3

2 y^{^{''}} - 7 y^{^{'}} + 5 y = 11 - 7 x - 16 x^{2} + 5 x^{3}

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{x} + x^{3} + x^{2} - x

Solution steps

2 y^{''} (x) - 7 y^{'} (x) + 5 y = 11 - 7 x - 16 x^{2} + 5 x^{3}

Solve linear ODE:

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{x} + x^{3} + x^{2} - x

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{x} + x^{3} + x^{2} - x

y^{^{''}} = y^{^{'}} + 2 x

y^{^{''}} + y^{^{'}} = 20

4 y^{^{''}} + 36 y = csc (3 x) x

y^{^{''}} + 16 y = 64 sin (x), y (0) = - 0.5, y^{^{'}} (0) = 0

4 y^{^{''}} - 4 y^{^{'}} + y = 5 e^{x} (sin (x) - cos (x))

What is the solution for 2y^{''}-7y^'+5y=11-7x-16x^2+5x^3 ?
The solution for 2y^{''}-7y^'+5y=11-7x-16x^2+5x^3 is y=c_{1}e^{(5x)/2}+c_{2}e^x+x^3+x^2-x