Internal problem ID [193]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y-6 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+2*y(x)=6*x,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\sqrt {2}\, x \right ) c_{2}+\cos \left (\sqrt {2}\, x \right ) c_{1}+3 x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[y''[x]+2*y[x]==6*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 x+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \\ \end{align*}