What is the solution for x^2(dy)/(dx)=xy+x^2e^{y/x} ?

The solution for x^2(dy)/(dx)=xy+x^2e^{y/x} is y=-xln(-ln(x)-c_{1})

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x^2(dy)/(dx)=xy+x^2e^{y/x}

x^{2} \frac{d y}{d x} = x y + x^{2} e^{\frac{y}{x}}

y = - x ln (- ln (x) - c_{1})

Solution steps

x^{2} \frac{d y}{d x} = x y + x^{2} e^{\frac{y}{x}}

Solve using substitution:

y = - x ln (- ln (x) - c_{1})

y = - x ln (- ln (x) - c_{1})

y^{^{''}} + 6 y + 8 = 0, y (0) = 0, y^{^{'}} (0) = 12

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

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What is the solution for x^2(dy)/(dx)=xy+x^2e^{y/x} ?
The solution for x^2(dy)/(dx)=xy+x^2e^{y/x} is y=-xln(-ln(x)-c_{1})