What is the solution for (dy)/(dx)=(1+2x)sqrt(y),y(0)=1 ?

The solution for (dy)/(dx)=(1+2x)sqrt(y),y(0)=1 is y=(x^2)/4+(x^3)/2+(x^4)/4+x+x^2+1

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(dy)/(dx)=(1+2x)sqrt(y),y(0)=1

\frac{d y}{d x} = (1 + 2 x) y, y (0) = 1

y = \frac{x ^{2}}{4} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + x + x^{2} + 1

Solution steps

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

Solve separable ODE:

y = \frac{x ^{2}}{4} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + x + x^{2} + 1

y = \frac{x ^{2}}{4} + \frac{x ^{3}}{2} + \frac{x ^{4}}{4} + x + x^{2} + 1

3 y^{^{'}} + 2 y = 0

x y^{^{'}} - y = 2

y^{^{'}} = - \frac{3 x ^{2}}{4 y}

y^{^{'}} = y cos (5 x), y (0) = 1

y^{^{'}} = - 2 - y + y^{2}

What is the solution for (dy)/(dx)=(1+2x)sqrt(y),y(0)=1 ?
The solution for (dy)/(dx)=(1+2x)sqrt(y),y(0)=1 is y=(x^2)/4+(x^3)/2+(x^4)/4+x+x^2+1