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Popular >

(dx)/(dt)=k+xr

Solution

\frac{d x}{d t} = k + x r

Solution

x = \frac{e ^{t r + c_{1} r}}{r} - \frac{k}{r}

Solution steps

\frac{d x}{d t} = k + x r

Solve separable ODE:

x = \frac{e ^{t r + c_{1} r}}{r} - \frac{k}{r}

x = \frac{e ^{t r + c_{1} r}}{r} - \frac{k}{r}

Popular Examples

derivative of f(x)=x^2cos^4(x)derivative of

f (x) = x^{2} cos^{4} (x)

integral of 4t^3

\int 4 t^{3} d t

integral of (x^2-1)/((x^3+x))

\int \frac{x ^{2} - 1}{( x ^{3} + x )} d x

derivative of x^4+8x^2-x

\frac{d}{d x} (x^{4} + 8 x^{2} - x)

integral from 2 to 3 of (3x^2+2x+3)

\int_{2}^{3} (3 x^{2} + 2 x + 3) d x

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=k+xr ?
The solution for (dx)/(dt)=k+xr is x=(e^{tr+c_{1}r})/r-k/r