23.2.49 problem 50

Internal problem ID [5404]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 50
Date solved : Tuesday, September 30, 2025 at 12:39:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}-4 \left (1+x \right ) y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 21

ode:=diff(y(x),x)^2-4*(1+x)*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \left (1+x \right )^{2} \\ y &= -\frac {c_1 \left (-4 x +c_1 -4\right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 27

ode=(D[y[x],x])^2-4*(1+x)*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{4} c_1 (-4 x-4+c_1)\\ y(x)&\to (x+1)^2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-4*x - 4)*Derivative(y(x), x) + 4*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out