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Popular >

(dy)/(dx)=xe^{-x}

Solution

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

Solution

y = - e^{- x} x - e^{- x} + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x e^{- x}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x e^{- x} d x

\int x e^{- x} d x = - e^{- x} x - e^{- x} + c_{1}

y = - e^{- x} x - e^{- x} + c_{1}

Popular Examples

integral from 0 to 7 of 5/3 x

\int_{0}^{7} \frac{5}{3} x d x

inverse oflaplace-1/(s^2+(5)^2)inverse laplace

- \frac{1}{s ^{2} + ( 5 ) ^{2}}

integral from-3 to 0 of sqrt(9-x^2)

\int_{- 3}^{0} 9 - x^{2} d x

inverse oflaplace (3s-1)/((s^2+2s+5))inverse laplace

\frac{3 s - 1}{( s ^{2} + 2 s + 5 )}

(dy)/(dx)=3(y^2+1),y(pi/4)=1

\frac{d y}{d x} = 3 (y^{2} + 1), y (\frac{π}{4}) = 1

Frequently Asked Questions (FAQ)

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