78.13.4 problem 1 (d)

Internal problem ID [18255]
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 (d)
Date solved : Monday, March 31, 2025 at 05:23:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \end{align*}

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

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+5*y(x) = 25*x^2+12; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \sin \left (2 x \right ) c_2 +{\mathrm e}^{x} \cos \left (2 x \right ) c_1 +5 x^{2}+4 x +2 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 35

ode=D[y[x],{x,2}] -2*D[y[x],x]+5*y[x]==25*x^2+12; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 x^2+4 x+c_2 e^x \cos (2 x)+c_1 e^x \sin (2 x)+2 \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-25*x**2 + 5*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 12,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 x^{2} + 4 x + \left (C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )}\right ) e^{x} + 2 \]