50.10.8 problem 1(h)

Internal problem ID [7977]
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 : Monday, January 27, 2025 at 03:34:57 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 27

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

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