What is the solution for (dy)/(dx)=2y+x^2+7 ?

The solution for (dy)/(dx)=2y+x^2+7 is y=-(x^2)/2-x/2-15/4+c_{1}e^{2x}

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(dy)/(dx)=2y+x^2+7

\frac{d y}{d x} = 2 y + x^{2} + 7

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} = 2 y + x^{2} + 7

Solve linear ODE:

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{15}{4} + c_{1} e^{2 x}

What is the solution for (dy)/(dx)=2y+x^2+7 ?
The solution for (dy)/(dx)=2y+x^2+7 is y=-(x^2)/2-x/2-15/4+c_{1}e^{2x}