78.13.8 problem 1 (h)

Internal problem ID [18330]
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 : Tuesday, January 28, 2025 at 11:46:49 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-2*diff(y(x),x)=12*x-10,y(x), singsol=all)
 

\[ y = \frac {c_{1} {\mathrm e}^{2 x}}{2}-3 x^{2}+2 x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 27

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

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