81.11.17 problem 15-16

Internal problem ID [21641]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-16
Date solved : Thursday, October 02, 2025 at 07:59:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 x^{2}+{\mathrm e}^{x}+2 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 37

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 2*x^2+exp(x)+2*x*exp(x)+4*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {7}{2}+{\mathrm e}^{2 x} c_1 +2 \,{\mathrm e}^{3 x}+\left (-x^{2}+c_2 -3 x \right ) {\mathrm e}^{x}+x^{2}+3 x \]

✓ Mathematica. Time used: 0.232 (sec). Leaf size: 47

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==2*x^2+Exp[x]+2*x*Exp[x]+4*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2-e^x \left (x^2+3 x+3-c_1\right )+3 x+2 e^{3 x}+c_2 e^{2 x}+\frac {7}{2} \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**2 - 2*x*exp(x) + 2*y(x) - 4*exp(3*x) - exp(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{2 x} + x^{2} + 3 x + \left (C_{1} - x^{2} - 3 x\right ) e^{x} + 2 e^{3 x} + \frac {7}{2} \]