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Popular >

(dy)/(dt)=ky

Solution

\frac{d y}{d t} = k y

Solution

y = e^{k t + c_{1}}

Solution steps

\frac{d y}{d t} = k y (t)

Solve separable ODE:

y = e^{k t + c_{1}}

y = e^{k t + c_{1}}

Graph

Popular Examples

(dy)/(dx)=2(1+x)(1+y^2),y(0)=0

\frac{d y}{d x} = 2 (1 + x) (1 + y^{2}), y (0) = 0

(dy)/(dx)=(2-y)sin(x)

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

x y^{^{'}} = (1 - x^{2}) y

(dz)/(dt)+4e^{t+z}=0

\frac{d z}{d t} + 4 e^{t + z} = 0

y^'+y/a = b/a ,y(0)=1

y^{^{'}} + \frac{y}{a} = \frac{b}{a}, y (0) = 1

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dt)=ky ?
The solution for (dy)/(dt)=ky is y=e^{kt+c_{1}}