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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 12 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

8 y^{^{''}} + y^{^{'}} - y = 0

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = - 2, y^{^{'}} (0) = - 3

y^{^{''}} + y = 0, y (0) = - 1

y^{^{''}} + 64 y = 0, y (π) = 0, y (0) = 0

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