71.7.10 problem 14

Internal problem ID [14360]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 14
Date solved : Monday, March 31, 2025 at 12:19:20 PM
CAS classification : [_linear]

\begin{align*} x^{2}-y+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \left (-x +c_1 \right ) x \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 13

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

\[ y(x)\to x (-x+c_1) \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = x \left (C_{1} - x\right ) \]