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Popular >

(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

(dx)/(dt)=t^3(1-x),x(0)=3

\frac{d x}{d t} = t^{3} (1 - x), x (0) = 3

derivative of 3x^{k-2}+2kx^{k-1}+4x^k

\frac{d}{d x} (3 x^{k - 2} + 2 k x^{k - 1} + 4 x^{k})

integral of x/((x-2)^3)

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

derivative of 1/4 e^x+3/4 e^{-x}

\frac{d}{d x} (\frac{1}{4} e^{x} + \frac{3}{4} e^{- x})

derivative of 5ln(x-(x^2)/(40))

\frac{d}{d x} (5 ln (x) - \frac{x ^{2}}{40})

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