(x^2+3)^2y=((2x(y^2+1)^2))/((x^2+3)y^')-(x^4+6x^2+9)y

Lösung

(x^{2} + 3)^{2} y = \frac{( 2 x ( y ^{2} + 1 ) ^{2} )}{( x ^{2} + 3 ) y ^{^{'}}} - (x^{4} + 6 x^{2} + 9) y

y = \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}, y = - \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}

Schritte zur Lösung

(x^{2} + 3)^{2} y = \frac{( 2 x ( y ^{2} + 1 ) ^{2} )}{( x ^{2} + 3 ) y ^{'} ( x )} - (x^{4} + 6 x^{2} + 9) y

Solve separable ODE:

y = \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}, y = - \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}

y = \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}, y = - \frac{- 2 x ^{4} - 4 c _{1} x ^{4} - 12 x ^{2} - 24 c _{1} x ^{2} - 36 c _{1} - 17}{- 1 + 4 c _{1} x ^{4} + 24 c _{1} x ^{2} + 36 c _{1}}

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

\frac{6 x d y}{d x} + y = x^{7}

\int 4 x^{3} e^{3 x^{4}} d x

\frac{d}{d x} (5 arctan (x - 1 + x^{2}))

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