Internal problem ID [5094]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page
1068
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{3}-3 y^{\prime } y^{2} x=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
dsolve((x^3+y(x)^3)=3*x*y(x)^2*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (x \left (x^{2}+2 c_{1} \right )\right )}^{\frac {1}{3}}}{2} \\ y \left (x \right ) &= -\frac {2^{\frac {2}{3}} {\left (x \left (x^{2}+2 c_{1} \right )\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (x \left (x^{2}+2 c_{1} \right )\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 90
DSolve[(x^3+y[x]^3)==3*x*y[x]^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [3]{-\frac {1}{2}} \sqrt [3]{x} \sqrt [3]{x^2+2 c_1} \\ y(x)\to \frac {\sqrt [3]{x} \sqrt [3]{x^2+2 c_1}}{\sqrt [3]{2}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x} \sqrt [3]{x^2+2 c_1}}{\sqrt [3]{2}} \\ \end{align*}