67.15.38 problem 22.10 (k)

Internal problem ID [16756]
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 : 22.10 (k)
Date solved : Thursday, October 02, 2025 at 01:38:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+5*y(x) = 10*x^2+4*x+8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_2 +{\mathrm e}^{2 x} \cos \left (x \right ) c_1 +2 x^{2}+4 x +4 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 35

ode=D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==10*x^2+4*x+8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^2+4 x+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x)+4 \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*x**2 - 4*x + 5*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x^{2} + 4 x + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{2 x} + 4 \]