89.28.4 problem 4

Internal problem ID [24892]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 229
Problem number : 4
Date solved : Thursday, October 02, 2025 at 10:49:09 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2} x -2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x*diff(y(x),x)^2-2*(y(x)+2*x)*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,x^{2} \\ y &= 4 x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 26

ode=x*D[y[x],x]^2-2*(y[x]+2*x)*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x^2\\ y(x)&\to 4 x+c_1\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x)**2 - (4*x + 2*y(x))*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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