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}

\int \frac{1}{8} sin (8 x) d x

\int \frac{5}{x} d x

g (x) = 6 x + 8

\int 2 x - y d x

x^{2} y^{^{'}} + y^{^{'}} = x y

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