Internal problem ID [2974]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 226.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-\left (1-x y^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 275
dsolve((1+x)*diff(y(x),x) = (1-x*y(x)^3)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )^{2}\right )^{\frac {1}{3}} \left (x +1\right )}{3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}} \\ y \relax (x ) = \left (-\frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )}-\frac {i \sqrt {3}\, 4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )}\right ) \left (x +1\right ) \\ y \relax (x ) = \left (-\frac {4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )}+\frac {i \sqrt {3}\, 4^{\frac {1}{3}} \left (\left (3 x^{4}+8 x^{3}+6 x^{2}+4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{6 x^{4}+16 x^{3}+12 x^{2}+8 c_{1}}\right ) \left (x +1\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 121
DSolve[(1+x) y'[x]==(1-x y[x]^3)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {(-2)^{2/3} (x+1)}{\sqrt [3]{-\left ((x (3 x+8)+6) x^2\right )-4 c_1}} \\ y(x)\to -\frac {2^{2/3} (x+1)}{\sqrt [3]{-\left ((x (3 x+8)+6) x^2\right )-4 c_1}} \\ y(x)\to \frac {(x+1) \text {Root}\left [\text {$\#$1}^3+4\&,3\right ]}{\sqrt [3]{-\left ((x (3 x+8)+6) x^2\right )-4 c_1}} \\ y(x)\to 0 \\ \end{align*}