8.8.6 problem 26(a.2)

Internal problem ID [843]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 26(a.2)
Date solved : Wednesday, February 05, 2025 at 04:34:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 31

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

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