What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x) ?

The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x) is y=c_{1}e^{2x}+c_{2}e^x+sin(x)+3cos(x)

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 10 sin (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + sin (x) + 3 cos (x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 10 sin (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + sin (x) + 3 cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + sin (x) + 3 cos (x)

\int 2 sin (x) d x

x \to 1 lim (- 2 x^{2} + 5 x + 4)

\int \frac{csc ^{2} ( 2 x )}{4 - cot ( 2 x )} d x

\int sin^{2} (x) cos (n x) d x

\frac{d}{d x} (\frac{cos ( x )}{2 x})

What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x) ?
The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x) is y=c_{1}e^{2x}+c_{2}e^x+sin(x)+3cos(x)