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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = - 3, y^{^{'}} (0) = 5

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

y = \frac{d ^{2} y}{d x ^{2}}

\frac{d ^{2} y}{d x ^{2}} + 7 \frac{d y}{d x} - 8 y = 0

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