What is the solution for (dy)/(dx)=-5sqrt(y) ?

The solution for (dy)/(dx)=-5sqrt(y) is y=(25x^2)/4-(5c_{1}x)/2+(c_{1}^2)/4

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(dy)/(dx)=-5sqrt(y)

\frac{d y}{d x} = - 5 y

y = \frac{25 x ^{2}}{4} - \frac{5 c _{1} x}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = - 5 y

Solve separable ODE:

y = \frac{25 x ^{2}}{4} - \frac{5 c _{1} x}{2} + \frac{c _{1}^{2}}{4}

y = \frac{25 x ^{2}}{4} - \frac{5 c _{1} x}{2} + \frac{c _{1}^{2}}{4}

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

x y^{2} - 2 y^{^{'}} y + y^{^{'}} = 0

\frac{d y}{d x} = \frac{y}{5}

d x = 6 \cdot 0.5 - 6 \cdot \frac{x}{50} d t

\frac{d y}{d t} = 0.07 (100 - y), y (0) = 25

What is the solution for (dy)/(dx)=-5sqrt(y) ?
The solution for (dy)/(dx)=-5sqrt(y) is y=(25x^2)/4-(5c_{1}x)/2+(c_{1}^2)/4