15.20.6 problem 6

Internal problem ID [3314]
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 : 6
Date solved : Tuesday, March 04, 2025 at 04:34:25 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left ({y^{\prime }}^{2}+1\right ) y&=2 y^{\prime } x \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 67

ode:=y(x)*(1+diff(y(x),x)^2) = 2*x*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= \sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (-2 i x +c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {c_{1} \left (2 i x +c_{1} \right )} \\ \end{align*}

✓ Mathematica. Time used: 3.155 (sec). Leaf size: 64

ode=(D[y[x],x]^2+1)*y[x]==2*D[y[x],x]*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to \sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to 0 \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + (Derivative(y(x), x)**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out