8.8.7 problem 26(b)

Internal problem ID [844]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 26(b)
Date solved : Wednesday, February 05, 2025 at 04:34:18 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: 0.004 (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: 0.015 (sec). Leaf size: 32

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

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