9.20.7 problem 7

Internal problem ID [3315]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 06:35:55 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 2 x +{y^{\prime }}^{2} x&=2 y^{\prime } y \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 35

ode:=2*x+diff(y(x),x)^2*x = 2*y(x)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {2}\, x \\ y &= -\sqrt {2}\, x \\ y &= \frac {2 c_1^{2}+x^{2}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 63

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

\[ \text {Solve}\left [\frac {1}{34} \left (\left (17+\sqrt {17}\right ) \log \left (\frac {4 y(x)}{x}+\sqrt {17}-1\right )-\left (\sqrt {17}-17\right ) \log \left (-\frac {4 y(x)}{x}+\sqrt {17}+1\right )\right )=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.465 (sec). Leaf size: 14

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

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