Internal problem ID [3236]
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: 112.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {5 y+{y^{\prime }}^{2}-x \left (x +y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 91
dsolve(5*y(x)+(diff(y(x),x))^2=x*(x+diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}}{4} \\ y \left (x \right ) &= x \sqrt {5}\, \sqrt {-c_{1}}-x^{2}+c_{1} \\ y \left (x \right ) &= -x \sqrt {5}\, \sqrt {-c_{1}}-x^{2}+c_{1} \\ y \left (x \right ) &= -x \sqrt {5}\, \sqrt {-c_{1}}-x^{2}+c_{1} \\ y \left (x \right ) &= x \sqrt {5}\, \sqrt {-c_{1}}-x^{2}+c_{1} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[5*y[x]+(y'[x])^2==x*(x+y'[x]),y[x],x,IncludeSingularSolutions -> True]
Timed out