What is the solution for (dy)/(dx)=4y+3e^{8x}(x+1),y(0)=1 ?

The solution for (dy)/(dx)=4y+3e^{8x}(x+1),y(0)=1 is y=3e^{8x}(x/4+3/16)+7/16 e^{4x}

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(dy)/(dx)=4y+3e^{8x}(x+1),y(0)=1

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1), y (0) = 1

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) + \frac{7}{16} e^{4 x}

Solution steps

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1)

Solve linear ODE:

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) + \frac{7}{16} e^{4 x}

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) + \frac{7}{16} e^{4 x}

\int (1 - 2 x)^{2} d x

\frac{d}{d θ} (4 - sin (θ))

\int \frac{1}{21 - 4 x - x ^{2}} d x

x e^{x}

x y^{^{'}} + y = - 5 x y^{2}, y (1) = 3

What is the solution for (dy)/(dx)=4y+3e^{8x}(x+1),y(0)=1 ?
The solution for (dy)/(dx)=4y+3e^{8x}(x+1),y(0)=1 is y=3e^{8x}(x/4+3/16)+7/16 e^{4x}