7.9.13 problem 26 (b)

Internal problem ID [261]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 26 (b)
Date solved : Wednesday, February 05, 2025 at 03:06:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y&=6 x +4 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+2*y(x)=6*x+4,y(x), singsol=all)
 

\[ y = \sin \left (\sqrt {2}\, x \right ) c_2 +\cos \left (\sqrt {2}\, x \right ) c_1 +3 x +2 \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]+2*y[x]==6*x+4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right )+2 \]