88.15.8 problem 8

Internal problem ID [24104]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 97
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:59:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=1+2 x +3 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 1+2*x+3*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{x} x c_1 +2 x +5+\frac {3 \,{\mathrm e}^{x} x^{2}}{2} \]

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 33

ode=D[y[x],{x,2}]-2*D[y[x],x]+y[x]==1+2*x+3*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 e^x x^2}{2}+x \left (2+c_2 e^x\right )+c_1 e^x+5 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = 2 x + \left (C_{1} + x \left (C_{2} + \frac {3 x}{2}\right )\right ) e^{x} + 5 \]