What is the solution for (dy)/(dx)=xy+7x+3y+21 ?

The solution for (dy)/(dx)=xy+7x+3y+21 is y=e^{(x^2)/2+3x+c_{1}}-7

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(dy)/(dx)=xy+7x+3y+21

\frac{d y}{d x} = x y + 7 x + 3 y + 21

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 7

Solution steps

\frac{d y}{d x} = x y + 7 x + 3 y + 21

Solve separable ODE:

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 7

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 7

What is the solution for (dy)/(dx)=xy+7x+3y+21 ?
The solution for (dy)/(dx)=xy+7x+3y+21 is y=e^{(x^2)/2+3x+c_{1}}-7