What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)=0 ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)=0 is y=c_{1}e^{4x}+c_{2}

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(d^2y)/(dx^2)-4(dy)/(dx)=0

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

y = c_{1} e^{4 x} + c_{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2}

y = c_{1} e^{4 x} + c_{2}

y^{^{''}} + 0.8 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 4

18 y^{^{''}} + 72 y = 0

10 x^{^{''}} + \frac{1}{90} x = 0, x (0) = 100, x^{^{'}} (0) = 25

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 8 y = 0

6 y^{^{''}} + 35 y = 0, y (0) = 3, y^{^{'}} (0) = 8

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)=0 ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)=0 is y=c_{1}e^{4x}+c_{2}