35.6.28 problem 34

Internal problem ID [6178]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 34
Date solved : Sunday, March 30, 2025 at 10:42:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

\[ y = {\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} c_1 +{\mathrm e}^{x}+x \]

✓ Mathematica. Time used: 0.26 (sec). Leaf size: 26

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

\[ y(x)\to x+e^x+c_1 e^{2 x}+c_2 e^{3 x} \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} e^{2 x} + C_{2} e^{3 x} + x + e^{x} \]