Internal problem ID [3503]
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]
\[ \boxed {3 x y^{\prime }-\left (2+y^{3} x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \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 \left (x \right ) = -\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 \left (x \right ) = -\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: 0.21 (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*}