What is the solution for (dy)/(dt)=-ksqrt(y) ?

The solution for (dy)/(dt)=-ksqrt(y) is y=(k^2t^2)/4-(c_{1}kt)/2+(c_{1}^2)/4

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(dy)/(dt)=-ksqrt(y)

\frac{d y}{d t} = - k y

y = \frac{k ^{2} t ^{2}}{4} - \frac{c _{1} k t}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d t} = - k y

Solve separable ODE:

y = \frac{k ^{2} t ^{2}}{4} - \frac{c _{1} k t}{2} + \frac{c _{1}^{2}}{4}

y = \frac{k ^{2} t ^{2}}{4} - \frac{c _{1} k t}{2} + \frac{c _{1}^{2}}{4}

9 x - 4 y (x^{2} + 1) (\frac{d y}{d x}) = 0

\int \frac{x}{( x + 4 ) ^{\frac{1}{3}}} d x

f (x) = e^{x} + 1

\frac{8 t}{t ^{2} + 9}

\frac{( x - 1 )}{( x + 1 )}

What is the solution for (dy)/(dt)=-ksqrt(y) ?
The solution for (dy)/(dt)=-ksqrt(y) is y=(k^2t^2)/4-(c_{1}kt)/2+(c_{1}^2)/4