What is the solution for (dy)/(dx)-y=3e^x+12e^{4x} ?

The solution for (dy)/(dx)-y=3e^x+12e^{4x} is y=3e^xx+4e^{4x}+c_{1}e^x

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(dy)/(dx)-y=3e^x+12e^{4x}

\frac{d y}{d x} - y = 3 e^{x} + 12 e^{4 x}

y = 3 e^{x} x + 4 e^{4 x} + c_{1} e^{x}

Solution steps

\frac{d y}{d x} - y = 3 e^{x} + 12 e^{4 x}

Solve linear ODE:

y = 3 e^{x} x + 4 e^{4 x} + c_{1} e^{x}

y = 3 e^{x} x + 4 e^{4 x} + c_{1} e^{x}

\int x^{2} \cdot 16 - x^{2} d x

\frac{d}{d x} (\frac{x - 15}{x - 15})

4 x + 8

x \to 1 lim (x - 3)

y = x \cdot e^{4 - x}

What is the solution for (dy)/(dx)-y=3e^x+12e^{4x} ?
The solution for (dy)/(dx)-y=3e^x+12e^{4x} is y=3e^xx+4e^{4x}+c_{1}e^x