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

The solution for (3xy+y^2)dx+(x^2+xy)dy=0 is y=(-x^2+sqrt(x^4+c_{1)})/x ,y=-(x^2+sqrt(x^4+c_{1)})/x

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(3xy+y^2)dx+(x^2+xy)dy=0

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

y = \frac{- x ^{2} + x ^{4} + c _{1}}{x}, y = - \frac{x ^{2} + x ^{4} + c _{1}}{x}

Solution steps

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

Solve using substitution:

y = \frac{- x ^{2} + x ^{4} + c _{1}}{x}, y = - \frac{x ^{2} + x ^{4} + c _{1}}{x}

y = \frac{- x ^{2} + x ^{4} + c _{1}}{x}, y = - \frac{x ^{2} + x ^{4} + c _{1}}{x}

\int_{3}^{5} \frac{1}{5 - x} d x

\frac{3.49}{x ^{0.432}}

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

f (x) = (e^{3 x} - 1)^{5}

c y^{- 9}

What is the solution for (3xy+y^2)dx+(x^2+xy)dy=0 ?
The solution for (3xy+y^2)dx+(x^2+xy)dy=0 is y=(-x^2+sqrt(x^4+c_{1)})/x ,y=-(x^2+sqrt(x^4+c_{1)})/x