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Popular >

x^'=ax+b

Solution

x^{^{'}} = a x + b

Solution

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

Solution steps

x^{'} (t) = a x (t) + b

Solve separable ODE:

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

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

Popular Examples

integral of xe^{(-x)/4}

\int x e^{\frac{- x}{4}} d x

derivative of (x^5-4x^2/(x^3))

\frac{d}{d x} (\frac{x ^{5} - 4 x ^{2}}{x ^{3}})

cos((ln(x+1))^2-e^{x^2})

cos ((ln (x + 1))^{2} - e^{x^{2}})

integral of (10)/(sqrt(x^2+16))

\int \frac{10}{x ^{2} + 16} d x

derivative of 1/15 cos^3(x(3cos^2(x)-5))

\frac{d}{d x} (\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5))

Frequently Asked Questions (FAQ)

What is the solution for x^'=ax+b ?
The solution for x^'=ax+b is x=(e^{ta+c_{1}a})/a-b/a