40.3.1 problem 23 (a)

Internal problem ID [6605]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (a)
Date solved : Sunday, March 30, 2025 at 11:12:09 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {x^{3}+3 c_1}{3 x} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^2}{3}+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.193 (sec). Leaf size: 10

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)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{3}}{3}}{x} \]