What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)-4y=0 ?

The solution for (d^2y)/(dx^2)+3(dy)/(dx)-4y=0 is y=c_{1}e^x+c_{2}e^{-4x}

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(d^2y)/(dx^2)+3(dy)/(dx)-4y=0

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 4 y = 0

Solve linear ODE:

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

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

y^{^{''}} + (e + 1) y^{^{'}} + ey = 0

3 y^{^{''}} - y^{^{'}} = 5 y

y^{^{''}} - y^{^{'}} - 42 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

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

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

What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)-4y=0 ?
The solution for (d^2y)/(dx^2)+3(dy)/(dx)-4y=0 is y=c_{1}e^x+c_{2}e^{-4x}