85.53.3 problem 1 (c)

Internal problem ID [22816]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 197
Problem number : 1 (c)
Date solved : Thursday, October 02, 2025 at 09:14:54 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

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

\[ y = \frac {x^{2}}{2}+\frac {x^{3}}{3}-{\mathrm e}^{-x} c_1 +\frac {{\mathrm e}^{3 x}}{12}-x +c_2 \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {x^3}{3}+\frac {x^2}{2}-x+\frac {e^{3 x}}{12}-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + \frac {x^{3}}{3} + \frac {x^{2}}{2} - x + \frac {e^{3 x}}{12} \]