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Popular Calculus >

(dy)/(dx)=e^{-3y}

Solution

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

Solution

y = \frac{ln ( 3 x + c _{1} )}{3}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( 3 x + c _{1} )}{3}

y = \frac{ln ( 3 x + c _{1} )}{3}

Graph

Popular Examples

(dp)/(dt)=k(600-p)

\frac{d p}{d t} = k (600 - p)

(dy)/(dx)y=(2x-9)/(5-3x)

\frac{d y}{d x} y = \frac{2 x - 9}{5 - 3 x}

(dv)/(dt)=0.075*v-9000

\frac{d v}{d t} = 0.075 \cdot v - 9000

x^'=-100x,x(0)=1

x^{^{'}} = - 100 x, x (0) = 1

(dy)/(dx)=3\sqrt[3]{y^2},y(0)=0

\frac{d y}{d x} = 3 3 y^{2}, y (0) = 0

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=e^{-3y} ?
The solution for (dy)/(dx)=e^{-3y} is y=(ln(3x+c_{1}))/3