28.1.91 problem 112

Internal problem ID [4397]
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
Date solved : Monday, January 27, 2025 at 09:14:16 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \end{align*}

✓ 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: 0.000 (sec). Leaf size: 0

DSolve[5*y[x]+(D[y[x],x])^2==x*(x+D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

Timed out