Internal problem ID [2995]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 247.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 y^{\prime } x -\left (2+x y^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 178
dsolve(3*x*diff(y(x),x) = (2+x*y(x)^3)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{-x^{3}+3 c_{1}} \\ y \relax (x ) = -\frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 c_{1}\right )}-\frac {i 3^{\frac {5}{6}} \left (x^{2} \left (-x^{3}+3 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 c_{1}\right )} \\ y \relax (x ) = -\frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 c_{1}\right )}+\frac {i 3^{\frac {5}{6}} \left (x^{2} \left (-x^{3}+3 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{-2 x^{3}+6 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 89
DSolve[3 x y'[x]==(2+x y[x]^3)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-3} x^{2/3}}{\sqrt [3]{-x^3+3 c_1}} \\ y(x)\to \frac {x^{2/3}}{\sqrt [3]{-\frac {x^3}{3}+c_1}} \\ y(x)\to \frac {(-1)^{2/3} x^{2/3}}{\sqrt [3]{-\frac {x^3}{3}+c_1}} \\ y(x)\to 0 \\ \end{align*}