73.9.5 problem 14.1 (e)

Internal problem ID [15195]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (e)
Date solved : Monday, March 31, 2025 at 01:31:02 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+3 y&={\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=x*diff(y(x),x)+3*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 x^{2}-2 x +1\right ) {\mathrm e}^{2 x}+4 c_1}{4 x^{3}} \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 30

ode=x*D[y[x],x]+3*y[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\int _1^xe^{2 K[1]} K[1]^2dK[1]+c_1}{x^3} \]

✓ Sympy. Time used: 0.315 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + 3*y(x) - exp(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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