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Popular Calculus >

y^'=ay+b

Solution

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

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Graph

Popular Examples

integral of 1/(x^2)x'

\int \frac{1}{x ^{2}} x^{'} d x

inverse oflaplace 6

in v erse l a pl a ce 6

taylor 1/x ,x=2

t a y l or \frac{1}{x}, x = 2

limit as x approaches 1-of x^2

x \to 1 - lim (x^{2})

derivative of sqrt(x)(x-3)^2

d er i v a t i v e x (x - 3)^{2}

Frequently Asked Questions (FAQ)

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