29.33.13 problem 975

Internal problem ID [5552]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 975
Date solved : Tuesday, March 04, 2025 at 10:00:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 45

ode:=y(x)^2*diff(y(x),x)^2-(1+x)*y(x)*diff(y(x),x)+x = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 72

ode=y[x]^2 (D[y[x],x])^2-(1+x)y[x] D[y[x],x]+x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.005 (sec). Leaf size: 44

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

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