Internal problem ID [2727]
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]]
Solve \begin {gather*} \boxed {5 y+\left (y^{\prime }\right )^{2}-x \left (x +y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 105
dsolve(5*y(x)+(diff(y(x),x))^2=x*(x+diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{4} \\ y \relax (x ) = \frac {3 x^{2}}{2}-\frac {x \left (5 x -2 \sqrt {-5 c_{1}}\right )}{2}+c_{1} \\ y \relax (x ) = \frac {3 x^{2}}{2}-\frac {x \left (5 x +2 \sqrt {-5 c_{1}}\right )}{2}+c_{1} \\ y \relax (x ) = \frac {3 x^{2}}{2}+\frac {x \left (-5 x -2 \sqrt {-5 c_{1}}\right )}{2}+c_{1} \\ y \relax (x ) = \frac {3 x^{2}}{2}+\frac {x \left (-5 x +2 \sqrt {-5 c_{1}}\right )}{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