84.10.2 problem 5.12

Internal problem ID [22130]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 5. Homogeneous differential equations. Supplementary problems
Problem number : 5.12
Date solved : Thursday, October 02, 2025 at 08:28:47 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = c_1 \,x^{2}-x \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 8

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

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