67.15.25 problem 22.9 (c)

Internal problem ID [16743]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.9 (c)
Date solved : Thursday, October 02, 2025 at 01:38:25 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

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

\[ y = -\frac {x^{2}}{16}+\frac {x^{3}}{12}-\frac {{\mathrm e}^{-4 x} c_1}{4}+\frac {x}{32}+c_2 \]

✓ Mathematica. Time used: 3.604 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to \int _1^xe^{-4 K[2]} \left (c_1+\int _1^{K[2]}e^{4 K[1]} K[1]^2dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 4 x} + \frac {x^{3}}{12} - \frac {x^{2}}{16} + \frac {x}{32} \]