What is the solution for (1+x^2)dy+(xy+x^3+x)dx=0 ?

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d y}{d x} = \frac{( 6 x - 2 x y ^{3} )}{y ^{2}}

2 x^{2} + 3 x - 2

f (t) = \frac{6 t + 38}{t + 9}

\int_{1}^{6} \frac{x ^{2} + 1}{7 x - x ^{2}} d x

\frac{d}{d x} (π x)

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