78.13.8 problem 1 (h)

Internal problem ID [18259]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (h)
Date solved : Monday, March 31, 2025 at 05:24:04 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: 0.086 (sec). Leaf size: 27

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

\[ y(x)\to -3 x^2+2 x+\frac {1}{2} c_1 e^{2 x}+c_2 \]

✓ Sympy. Time used: 0.143 (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)
 

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