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]]
\[ \boxed {y^{\prime \prime }+4 y-\ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 65
dsolve(diff(y(x),x$2)+4*y(x)=ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} +\frac {i \pi \cos \left (2 x \right ) \left (\operatorname {csgn}\left (x \right )-1\right ) \operatorname {csgn}\left (i x \right )}{8}-\frac {\cos \left (2 x \right ) \operatorname {Ci}\left (2 x \right )}{4}+\frac {\left (\pi \,\operatorname {csgn}\left (x \right )-2 \,\operatorname {Si}\left (2 x \right )\right ) \sin \left (2 x \right )}{8}+\frac {\ln \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.018 (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) (-\operatorname {CosIntegral}(2 x)+4 c_1)+\sin (2 x) (-\text {Si}(2 x)+4 c_2)+\log (x)) \\ \end{align*}