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

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

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

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

y = tan (\frac{x ^{2}}{2} + c_{1}) x

Solution steps

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

Solve using substitution:

y = tan (\frac{x ^{2}}{2} + c_{1}) x

y = tan (\frac{x ^{2}}{2} + c_{1}) x

\int \frac{18}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

n = 0 \sum \infty \frac{5 ^{n + 1}}{4 ^{n} ( 3 n - 1 ) !}

x \to 4 lim (- \frac{1}{x ^{\frac{3}{2}}})

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

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

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