What is the solution for y^{''}-3y^'+2y=11e^3x,y^1(0)=ex ?

The solution for y^{''}-3y^'+2y=11e^3x,y^1(0)=ex is y=c_{1}e^{2x}+c_{2}e^x+(11e^3x)/2+(33e^3)/4

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y^{''}-3y^'+2y=11e^3x,y^1(0)=ex

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3} x, y^{1} (0) = e x

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{11 e ^{3} x}{2} + \frac{33 e ^{3}}{4}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 11 e^{3} x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{11 e ^{3} x}{2} + \frac{33 e ^{3}}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{11 e ^{3} x}{2} + \frac{33 e ^{3}}{4}

y^{^{''}} + 4 y = 8 x^{2} + 7 x

y^{^{''}} - 4 y^{^{'}} = x

10 y^{^{''}} + 90 y^{^{'}} + \frac{1}{0.005} y = 500 sin (x)

y^{^{''}} + 3 y = cos (3 x)

y^{^{''}} + 3 y^{^{'}} = 9

What is the solution for y^{''}-3y^'+2y=11e^3x,y^1(0)=ex ?
The solution for y^{''}-3y^'+2y=11e^3x,y^1(0)=ex is y=c_{1}e^{2x}+c_{2}e^x+(11e^3x)/2+(33e^3)/4