67.2.11 problem Problem 1(k)

Internal problem ID [13897]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(k)
Date solved : Monday, March 31, 2025 at 08:17:21 AM
CAS classification : [_separable]

\begin{align*} 5 y^{\prime }-x y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=5*diff(y(x),x)-x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {x^{2}}{10}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 22

ode=5*D[y[x],x]-x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 e^{\frac {x^2}{10}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.260 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + 5*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x^{2}}{10}} \]