Internal problem ID [15051]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 158.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {3 y^{2} x y^{\prime }-2 y^{3}=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve(3*x*y(x)^2*diff(y(x),x)-2*y(x)^3=x^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (\left (x +c_{1} \right ) x^{2}\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\left (x +c_{1} \right ) x^{2}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (\left (x +c_{1} \right ) x^{2}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 66
DSolve[3*x*y[x]^2*y'[x]-2*y[x]^3==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{2/3} \sqrt [3]{x+c_1} \\ y(x)\to -\sqrt [3]{-1} x^{2/3} \sqrt [3]{x+c_1} \\ y(x)\to (-1)^{2/3} x^{2/3} \sqrt [3]{x+c_1} \\ \end{align*}