Practice problem
Solve the differential equation
ydydx=xe−xy\frac{dy}{dx} = xe^{-x}ydxdy=xe−x
for the initial condition y(0)=4y(0) = 4y(0)=4
y(x)=2e−x(−x+9ex−1)y(x)=\sqrt2\sqrt{e^{-x}(-x+9e^x-1)}y(x)=2e−x(−x+9ex−1)
y(x)=2e−2x(−2x+7ex−3)y(x)=\sqrt2\sqrt{e^{-2x}(-2x+7e^x-3)}y(x)=2e−2x(−2x+7ex−3)
y(x)=2e−x(−3x+4ex−5)y(x)=\sqrt2\sqrt{e^{-x}(-3x+4e^x-5)}y(x)=2e−x(−3x+4ex−5)
Type a concept, like “slope” or “photosynthesis”.
