44.10.8 problem 1(h)

Internal problem ID [9263]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 1(h)
Date solved : Tuesday, September 30, 2025 at 06:15:48 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x) = 12*x-10; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 2.773 (sec). Leaf size: 47

ode=D[y[x],{x,2}]-2*D[y[x],x]==12*x-10; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^xe^{2 K[2]} \left (c_1+\int _1^{K[2]}2 e^{-2 K[1]} (6 K[1]-5)dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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