What is the solution for (2x-y)dx+(2y-x)dy=0,y(1)=3 ?

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

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(2x-y)dx+(2y-x)dy=0,y(1)=3

(2 x - y) d x + (2 y - x) d y = 0, y (1) = 3

y = \frac{x + - 3 x ^{2} + c _{1}}{2}, y = \frac{x - - 3 x ^{2} + c _{1}}{2}

Solution steps

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

Solve exact ODE:

y = \frac{x + - 3 x ^{2} + c _{1}}{2}, y = \frac{x - - 3 x ^{2} + c _{1}}{2}

y = \frac{x + - 3 x ^{2} + c _{1}}{2}, y = \frac{x - - 3 x ^{2} + c _{1}}{2}

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