What is the solution for (dy)/(dx)=20+28x+40y+56xy ?

The solution for (dy)/(dx)=20+28x+40y+56xy is y=(e^{8((7x^2)/2+5x)+c_{1}})/(2)-1/2

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(dy)/(dx)=20+28x+40y+56xy

\frac{d y}{d x} = 20 + 28 x + 40 y + 56 x y

y = \frac{e ^{8 (\frac{7 x ^{2}}{2} + 5 x) + c_{1}}}{2} - \frac{1}{2}

Solution steps

\frac{d y}{d x} = 20 + 28 x + 40 y + 56 x y

Solve separable ODE:

y = \frac{e ^{8 (\frac{7 x ^{2}}{2} + 5 x) + c_{1}}}{2} - \frac{1}{2}

y = \frac{e ^{8 (\frac{7 x ^{2}}{2} + 5 x) + c_{1}}}{2} - \frac{1}{2}

What is the solution for (dy)/(dx)=20+28x+40y+56xy ?
The solution for (dy)/(dx)=20+28x+40y+56xy is y=(e^{8((7x^2)/2+5x)+c_{1}})/(2)-1/2