What is the solution for (dy)/(dx)=2y+x^2+5 ?

The solution for (dy)/(dx)=2y+x^2+5 is y=-(x^2)/2-x/2-11/4+c_{1}e^{2x}

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(dy)/(dx)=2y+x^2+5

\frac{d y}{d x} = 2 y + x^{2} + 5

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{11}{4} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} = 2 y + x^{2} + 5

Solve linear ODE:

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{11}{4} + c_{1} e^{2 x}

y = - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{11}{4} + c_{1} e^{2 x}

\frac{d y}{d x} + (\frac{4}{x}) y = 4 x + 9

l a pl a ce t r an s f or m 2 e^{4 t}

t an g e n t x^{4}

\int 2 x e^{2 x} d x

\int_{1}^{2} \frac{x ^{5} + 5 x ^{8}}{x ^{4}} d x

What is the solution for (dy)/(dx)=2y+x^2+5 ?
The solution for (dy)/(dx)=2y+x^2+5 is y=-(x^2)/2-x/2-11/4+c_{1}e^{2x}