What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=0 ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=0 is y=c_{1}e^{3x}+c_{2}xe^{3x}

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(d^2y)/(dx^2)-6(dy)/(dx)+9y=0

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 0

Solve linear ODE:

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

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

t an g e n t \frac{e ^{x}}{x + 4}

\frac{d}{d x} (x^{3} + x^{2} - 8 x + 7)

\int 2^{u} d u

y^{^{''}} - y^{^{'}} + 289 y = 17 sin (17 t)

a re a x = y^{4}, x = y^{5}

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=0 ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+9y=0 is y=c_{1}e^{3x}+c_{2}xe^{3x}