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Popular >

(dy)/(dt)+ay=b

Solution

\frac{d y}{d t} + a y = b

Solution

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

Solution steps

\frac{d y}{d t} + a y (t) = b

Solve separable ODE:

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

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

Popular Examples

tangent of 2sqrt(x)tangent of

2 x

derivative of (x^4+36x^2)/((x^2+12)^2)derivative of

\frac{x ^{4} + 36 x ^{2}}{( x ^{2} + 12 ) ^{2}}

limit as x approaches 2 of e^{x^2-2x}

x \to 2 lim (e^{x^{2} - 2 x})

integral of x/(5x-4)

\int \frac{x}{5 x - 4} d x

integral of x(sqrt(a^2-x^2))

\int x (a^{2} - x^{2}) d x

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dt)+ay=b ?
The solution for (dy)/(dt)+ay=b is y=-(e^{-at-c_{1}a})/a+b/a