Internal problem ID [4586]
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]
Solve \begin {gather*} \boxed {x^{3}+y^{3}-3 x y^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 90
dsolve((x^3+y(x)^3)=3*x*y(x)^2*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (4 x^{3}+8 c_{1} x \right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (4 x^{3}+8 c_{1} x \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (4 x^{3}+8 c_{1} x \right )^{\frac {1}{3}}}{4} \\ y \relax (x ) = -\frac {\left (4 x^{3}+8 c_{1} x \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (4 x^{3}+8 c_{1} x \right )^{\frac {1}{3}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.188 (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*}