What is the solution for (dy)/(dx)=(1+4x)(sqrt(y)) ?

The solution for (dy)/(dx)=(1+4x)(sqrt(y)) is y=(x^2)/4+(c_{1}x)/2+(c_{1}^2)/4+x^3+c_{1}x^2+x^4

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(dy)/(dx)=(1+4x)(sqrt(y))

\frac{d y}{d x} = (1 + 4 x) (y)

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

Solution steps

\frac{d y}{d x} = (1 + 4 x) (y)

Solve separable ODE:

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

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

e^{x + y} d y - d x = 0

x^{^{'}} = 1 - 0.4 x

\frac{1}{y} \cdot \frac{d y}{d x} = 10

\frac{d x}{d y} = 0.2 x y

y^{^{'}} + \frac{3}{2} y = \frac{3}{2}

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