Internal problem ID [3229]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 87.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{3}+y^{2}-y^{\prime } y x=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 269
dsolve((diff(y(x),x))^3+y(x)^2=x*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {2 x^{4}}{81 \left (\frac {x}{3}-\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}-\frac {2 x^{3} \sqrt {x^{2}+3 c_{1}}}{81 \left (\frac {x}{3}-\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}-\frac {c_{1} x^{2}}{27 \left (\frac {x}{3}-\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}+\frac {2 c_{1} x \sqrt {x^{2}+3 c_{1}}}{27 \left (\frac {x}{3}-\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}+\frac {c_{1}^{2}}{3 x -3 \sqrt {x^{2}+3 c_{1}}} y \left (x \right ) = \frac {2 x^{4}}{81 \left (\frac {x}{3}+\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}+\frac {2 x^{3} \sqrt {x^{2}+3 c_{1}}}{81 \left (\frac {x}{3}+\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}-\frac {c_{1} x^{2}}{27 \left (\frac {x}{3}+\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}-\frac {2 c_{1} x \sqrt {x^{2}+3 c_{1}}}{27 \left (\frac {x}{3}+\frac {\sqrt {x^{2}+3 c_{1}}}{3}\right )}+\frac {c_{1}^{2}}{3 x +3 \sqrt {x^{2}+3 c_{1}}} \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3+y[x]^2==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
Timed out