What is the solution for (dx)/(dt)=-ksqrt(x),x(0)=5 ?

The solution for (dx)/(dt)=-ksqrt(x),x(0)=5 is x=(k^2t^2)/4-sqrt(5)kt+5

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(dx)/(dt)=-ksqrt(x),x(0)=5

\frac{d x}{d t} = - k x, x (0) = 5

x = \frac{k ^{2} t ^{2}}{4} - 5 k t + 5

Solution steps

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

Solve separable ODE:

x = \frac{k ^{2} t ^{2}}{4} - 5 k t + 5

x = \frac{k ^{2} t ^{2}}{4} - 5 k t + 5

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

\frac{d x}{d t} = - 300 \cdot \frac{x}{1 0 ^{8}}

y^{^{'}} + \frac{x}{1 + x ^{2}} \cdot y = \frac{2 x}{1 + x ^{2}}

\frac{d y}{d x} + 9 x y = 8 x, y (0) = 2

\frac{d y}{d x} + 9 x y = 8 x, y (0) = 5

What is the solution for (dx)/(dt)=-ksqrt(x),x(0)=5 ?
The solution for (dx)/(dt)=-ksqrt(x),x(0)=5 is x=(k^2t^2)/4-sqrt(5)kt+5