29.29.10 problem 832

Internal problem ID [5415]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 832
Date solved : Sunday, March 30, 2025 at 08:10:51 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 22

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

\begin{align*} y &= -\frac {\left (-1+x \right )^{2}}{8} \\ y &= c_1 \left (2 c_1 +x -1\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 28

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

\begin{align*} y(x)\to c_1 (x-1+2 c_1) \\ y(x)\to -\frac {1}{8} (x-1)^2 \\ \end{align*}

✓ Sympy. Time used: 2.236 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = 2 C_{1}^{2} - C_{1} x + \frac {x}{4} - \frac {1}{8} \]