What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=2x ?

The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=2x is y=c_{1}e^{2x}+c_{2}e^x+x+3/2

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=2x

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + y = sec (x) tan (x)

y^{^{''}} + y + y = \frac{( e ^{t} )}{t}

x y^{^{'''}} - 4 x y^{^{'}} + 2 x y = cos (x)

x^{^{''}} - 4 x^{^{'}} + 3 x = t e^{t}

y^{^{''}} - 4 y^{^{'}} + 3 y = 13 cos (2 x)

What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=2x ?
The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=2x is y=c_{1}e^{2x}+c_{2}e^x+x+3/2