What is the solution for (x+y)dx+(x+2y)dy=0,y(2)=3 ?

The solution for (x+y)dx+(x+2y)dy=0,y(2)=3 is y=(-x+sqrt(-x^2+c_{1)})/2 ,y=-(x+sqrt(-x^2+c_{1)})/2

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(x+y)dx+(x+2y)dy=0,y(2)=3

(x + y) d x + (x + 2 y) d y = 0, y (2) = 3

y = \frac{- x + - x ^{2} + c _{1}}{2}, y = - \frac{x + - x ^{2} + c _{1}}{2}

Solution steps

(x + y) d x + (x + 2 y) d y = 0

Solve exact ODE:

y = \frac{- x + - x ^{2} + c _{1}}{2}, y = - \frac{x + - x ^{2} + c _{1}}{2}

y = \frac{- x + - x ^{2} + c _{1}}{2}, y = - \frac{x + - x ^{2} + c _{1}}{2}

x \to 0 - lim (\frac{1}{1 + e ^{\frac{1}{x}}})

\frac{d}{d x} (2 arctan (4 x))

x \to 0 lim (x^{2} ln (x^{2}))

\int \frac{1}{( x ^{2} - 16 ) ^{\frac{3}{2}}} d x

\int x^{\frac{3}{2}} ln (x) d x

What is the solution for (x+y)dx+(x+2y)dy=0,y(2)=3 ?
The solution for (x+y)dx+(x+2y)dy=0,y(2)=3 is y=(-x+sqrt(-x^2+c_{1)})/2 ,y=-(x+sqrt(-x^2+c_{1)})/2