y2xeyxyx find the solutionSolutionlet yx t y tx y txdtd

y\'=(2xe^(y/x)+y)/x find the solution

let y/x = t

=> y = tx

=> y` = t+xdt/dx

so, equation becomes

t+xdt/dx = (2e^t+t)

xdt/dx = 2e^t

dt/e^t= 2dx/x

integrate on both sides

-e^-t = 2ln(cx) (where c is constant)

t= -ln(ln(cx)^2))

y/x = -ln(ln(cx)^2))

=> y = -x*ln(ln(cx)^2))

$y\'=(2xe^(y/x)+y)/x find the solutionSolutionlet y/x = t => y = tx => y` = t+xdt/dx so, equation becomes t+xdt/dx = (2e^t+t) xdt/dx = 2e^t dt/e^t= 2dx/x i$

y2xeyxyx find the solutionSolutionlet yx t y tx y txdtd

Solution

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