What is the solution for (5x+ye^{y/x})dx-xe^{y/x}dy=0 ?

The solution for (5x+ye^{y/x})dx-xe^{y/x}dy=0 is y=ln(5ln(x)+c_{1})x

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(5x+ye^{y/x})dx-xe^{y/x}dy=0

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

y = ln (5 ln (x) + c_{1}) x

Solution steps

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

Solve using substitution:

y = ln (5 ln (x) + c_{1}) x

y = ln (5 ln (x) + c_{1}) x

y^{^{'}} = \frac{y}{x} + (\frac{2 x ^{3}}{y}) cos (x^{2})

x \to 0 lim ((2 x - 1)^{3})

x \to 9 - lim (\frac{- 3}{( x - 9 ) ^{2}})

\int_{- 1}^{1} 1 - y^{2} - (y^{2} - 1) d y

(3, - 2), (4, - 7)

What is the solution for (5x+ye^{y/x})dx-xe^{y/x}dy=0 ?
The solution for (5x+ye^{y/x})dx-xe^{y/x}dy=0 is y=ln(5ln(x)+c_{1})x