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Popular >

x^'+kx=1

Solution

x^{^{'}} + k x = 1

Solution

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

Solution steps

x^{'} (t) + k x (t) = 1

Solve separable ODE:

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

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

Popular Examples

(dy)/(dx)-(x/(2sqrt(y)))=0

\frac{d y}{d x} - (\frac{x}{2 y}) = 0

(y^2dy)/(y^3-4)=(xdx)/(x^2+2)

\frac{y ^{2} d y}{y ^{3} - 4} = \frac{x d x}{x ^{2} + 2}

(dr)/(dt)=0.1872*r,r(0)=24

\frac{d r}{d t} = 0.1872 \cdot r, r (0) = 24

sqrt(1+x^3)y^'=x^2y+x^2

1 + x^{3} y^{^{'}} = x^{2} y + x^{2}

y^'=-y/x ,y(1)=3

y^{^{'}} = - \frac{y}{x}, y (1) = 3

Frequently Asked Questions (FAQ)

What is the solution for x^'+kx=1 ?
The solution for x^'+kx=1 is x=-(e^{-kt-c_{1}})/k+1/k