What is the solution for (dy)/(dx)=(1+x+x^2)y ?

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

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(dy)/(dx)=(1+x+x^2)y

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = 7 e^{3 x - 5 y}

\frac{d V}{d t} = (10 - \frac{4}{100} V), V (0) = 0

\frac{d v}{df} = v \cdot f

y e^{x} \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

y = \frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}} \frac{d y}{d x}

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