Internal problem ID [15153]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 291.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {x y^{2} y^{\prime }-y^{3}=\frac {x^{4}}{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve(x*y(x)^2*diff(y(x),x)-y(x)^3=1/3*x^4,y(x), singsol=all)
\begin{align*} y &= \left (x +c_{1} \right )^{\frac {1}{3}} x \\ y &= -\frac {\left (x +c_{1} \right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) x}{2} \\ y &= \frac {\left (x +c_{1} \right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 54
DSolve[x*y[x]^2*y'[x]-y[x]^3==1/3*x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt [3]{x+c_1} \\ y(x)\to -\sqrt [3]{-1} x \sqrt [3]{x+c_1} \\ y(x)\to (-1)^{2/3} x \sqrt [3]{x+c_1} \\ \end{align*}