32.8.24 problem Exercise 21.32, page 231

Internal problem ID [5973]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.32, page 231
Date solved : Sunday, March 30, 2025 at 10:28:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{x} \left (2 x -3\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 11

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = exp(x)*(2*x-3); 
ic:=y(0) = 1, D(y)(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 35

ode=D[y[x],{x,2}]-5*D[y[x],x]-6*y[x]==Exp[x]*(2*x-3); 
ic={y[0]==1,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{175} e^{-x} \left (-7 e^{2 x} (5 x-9)+87 e^{7 x}+25\right ) \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3 - 2*x)*exp(x) + 6*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (x + e^{x}\right ) e^{x} \]