What is the solution for (dy)/(dx)=7xsqrt(y) ?

The solution for (dy)/(dx)=7xsqrt(y) is y=(49x^4}{16}+\frac{7c_{1}x^2)/4+(c_{1}^2)/4

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(dy)/(dx)=7xsqrt(y)

\frac{d y}{d x} = 7 x y

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 7 x y

Solve separable ODE:

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

x \to - 1 lim (\frac{sin ( x )}{x})

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

\frac{125}{x ^{2} + 25}

\frac{d}{d x} (x^{4} - 4 x^{2} + 2)

\frac{\partial}{\partial x} (- (x^{2} + y^{2}))

What is the solution for (dy)/(dx)=7xsqrt(y) ?
The solution for (dy)/(dx)=7xsqrt(y) is y=(49x^4}{16}+\frac{7c_{1}x^2)/4+(c_{1}^2)/4