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Popular >

(dx)/(dt)=a-bx

Solution

\frac{d x}{d t} = a - b x

Solution

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

Solution steps

\frac{d x}{d t} = a - b x (t)

Solve separable ODE:

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

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

Popular Examples

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

(dy)/(dx)=(y^2+xy^2)/(x^2y-x^2)

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

3e^xtan(y)dx+(1-e^x)sec^2(y)dy=0

3 e^{x} tan (y) d x + (1 - e^{x}) sec^{2} (y) d y = 0

(dy)/(dx)=ye^{3x}

\frac{d y}{d x} = y e^{3 x}

(dy)/(dx)=y^2-3y+2

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

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)=a-bx ?
The solution for (dx)/(dt)=a-bx is x=-(e^{-bt-c_{1}b})/b+a/b