What is the solution for y^{''}-4y^'+3y=3x^2-5x+1 ?

The solution for y^{''}-4y^'+3y=3x^2-5x+1 is y=c_{1}e^{3x}+c_{2}e^x+x^2+x+1

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y^{''}-4y^'+3y=3x^2-5x+1

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 x^{2} - 5 x + 1

y = c_{1} e^{3 x} + c_{2} e^{x} + x^{2} + x + 1

Solution steps

y^{''} (x) - 4 y^{'} (x) + 3 y = 3 x^{2} - 5 x + 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} + x^{2} + x + 1

y = c_{1} e^{3 x} + c_{2} e^{x} + x^{2} + x + 1

\int \frac{4 x ^{2} + 2}{1 + x ^{2}} d x

\int_{1}^{5} \frac{3}{x ^{2}} d x

x^{2} y^{^{''}} - 4 x y^{^{'}} + 6 y = 0

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 3

\frac{\partial}{\partial x} (2 (x - y) e^{2 y + x^{2}})

What is the solution for y^{''}-4y^'+3y=3x^2-5x+1 ?
The solution for y^{''}-4y^'+3y=3x^2-5x+1 is y=c_{1}e^{3x}+c_{2}e^x+x^2+x+1