What is the solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} ?

The solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} is y=c_{1}e^x+c_{2}e^{-(4x)/3}+1/2 e^{-3x}

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3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x}

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

y = c_{1} e^{x} + c_{2} e^{- \frac{4 x}{3}} + \frac{1}{2} e^{- 3 x}

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- \frac{4 x}{3}} + \frac{1}{2} e^{- 3 x}

y = c_{1} e^{x} + c_{2} e^{- \frac{4 x}{3}} + \frac{1}{2} e^{- 3 x}

What is the solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} ?
The solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} is y=c_{1}e^x+c_{2}e^{-(4x)/3}+1/2 e^{-3x}