Solve this differential equation dydx yx eyxSolutionWe try

Solve this differential equation, dy/dx = y/x - e^-y/x

We try the substitution

u=y/x

y=ux

y\'=u+u\'x

Substituting gives

u+u\'x=u-e^{-u}

u\'x=-e^{-u}

e^uu\'=-1/x

e^udu=-dx/x

Integrating gives

e^u=-ln(x)+C

u=ln(-ln(x)+c)

y/x=ln(-ln(x)+c)

$Solve this differential equation, dy/dx = y/x - e^-y/xSolutionWe try the substitution u=y/x y=ux y\'=u+u\'x Substituting gives u+u\'x=u-e^{-u} u\'x=-e^{-u} e^u$

Solve this differential equation dydx yx eyxSolutionWe try

Solution

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