What is the solution for (dy)/(dx)=xy+5x+3y+15 ?

The solution for (dy)/(dx)=xy+5x+3y+15 is y=e^{(x^2)/2+3x+c_{1}}-5

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(dy)/(dx)=xy+5x+3y+15

\frac{d y}{d x} = x y + 5 x + 3 y + 15

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 5

Solution steps

\frac{d y}{d x} = x y + 5 x + 3 y + 15

Solve separable ODE:

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 5

y = e^{\frac{x ^{2}}{2} + 3 x + c_{1}} - 5

y^{^{'}} + \frac{1}{1 - x ^{2}} y = \frac{3}{1 - x ^{2}}

y^{^{'}} - 3 y = - 4

(x + 1) d x = \frac{1}{- y ^{2}} d y

y^{^{'}} = \frac{( y ^{2} + 1 )}{( x ^{2} + 1 )}

(2 t - 1) y^{^{'}} - 4 y = 0

What is the solution for (dy)/(dx)=xy+5x+3y+15 ?
The solution for (dy)/(dx)=xy+5x+3y+15 is y=e^{(x^2)/2+3x+c_{1}}-5