Internal problem ID [5254]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]
\[ \boxed {y^{3}+3 y^{\prime } y^{2} x=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 92
dsolve((x^3+y(x)^3)+3*x*y(x)^2*diff(y(x),x)= 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2^{\frac {1}{3}} {\left (-\left (x^{4}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {2^{\frac {1}{3}} {\left (-\left (x^{4}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} {\left (-\left (x^{4}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 99
DSolve[(x^3+y[x]^3)+3*x*y[x]^2*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-x^4+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^4+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^4+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ \end{align*}