78.13.4 problem 1 (d)

Internal problem ID [18326]
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 : Tuesday, January 28, 2025 at 11:46:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

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

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

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