What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=0 ?

The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=0 is y=c_{1}e^{2x}+c_{2}e^x

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=0

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = 0

(D^{4} - D^{3} - 3 D^{2} + D + 2) y = 0

y^{^{''}} + 4 y^{^{'}} + 6 y = 0

\frac{d ^{4} y}{d x ^{4}} - 23 \frac{d ^{2} y}{d x ^{2}} - 50 y = 0

What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=0 ?
The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=0 is y=c_{1}e^{2x}+c_{2}e^x