Internal problem ID [2326]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page
575
Problem number: Problem 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 64
dsolve(diff(y(x),x$2)+4*y(x)=ln(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {\left (i \pi \left (\mathrm {csgn}\relax (x )-1\right ) \mathrm {csgn}\left (i x \right )-2 \cosineIntegral \left (2 x \right )\right ) \cos \left (2 x \right )}{8}+\frac {\left (\pi \,\mathrm {csgn}\relax (x )-2 \sinIntegral \left (2 x \right )\right ) \sin \left (2 x \right )}{8}+\frac {\ln \relax (x )}{4} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 44
DSolve[y''[x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} (\cos (2 x) (-\text {CosIntegral}(2 x)+4 c_1)+\sin (2 x) (-\text {Si}(2 x)+4 c_2)+\log (x)) \\ \end{align*}