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 : Tuesday, March 04, 2025 at 06:39:11 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 91

ode:=5*y(x)+diff(y(x),x)^2 = x*(x+diff(y(x),x)); 
dsolve(ode,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*}

✗ Mathematica

ode=5*y[x]+(D[y[x],x])^2==x*(x+D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✓ Sympy. Time used: 4.382 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x + Derivative(y(x), x)) + 5*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{4} - \frac {5 \left (C_{1} + x\right )^{2}}{4} \]