What is the integral of y-y/(x^2)e^{y/x} ?

The integral of y-y/(x^2)e^{y/x} is yx+e^{y/x}+C

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integral of y-y/(x^2)e^{y/x}

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

y x + e^{\frac{y}{x}} + C

Solution steps

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int y d x - \int \frac{y}{x ^{2}} e^{\frac{y}{x}} d x

\int y d x = y x

\int \frac{y}{x ^{2}} e^{\frac{y}{x}} d x = - e^{\frac{y}{x}}

= y x - (- e^{\frac{y}{x}})

Simplify

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

Add a constant to the solution

= y x + e^{\frac{y}{x}} + C

(tan (x))^{x}

x^{3} y^{^{'}} + 2 x^{2} y = - 2 cos (4 x) y^{- \frac{1}{2}}

y^{3} d x + 3 x y^{2} d y = 0

\int \frac{( 2 x ^{2} + 5 )}{x ^{2} + 1} d x

x \to \infty lim (x + 6)

What is the integral of y-y/(x^2)e^{y/x} ?
The integral of y-y/(x^2)e^{y/x} is yx+e^{y/x}+C