35.8.16 problem 16

Internal problem ID [6223]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 16
Date solved : Sunday, March 30, 2025 at 10:43:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 +{\mathrm e}^{x} c_1 -x \right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (-x+c_2 e^x-1+c_1\right ) \]

✓ Sympy. Time used: 0.202 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - exp(2*x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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