Internal problem ID [2835]
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]]
\[ \boxed {y^{\prime \prime }+4 y=\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)+4*y(x)=ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {i \cos \left (2 x \right ) \pi \left (-1+\operatorname {csgn}\left (x \right )\right ) \operatorname {csgn}\left (i x \right )}{8}+\frac {\left (8 c_{1} -2 \,\operatorname {Ci}\left (2 x \right )\right ) \cos \left (2 x \right )}{8}+\frac {\left (\pi \,\operatorname {csgn}\left (x \right )+8 c_{2} -2 \,\operatorname {Si}\left (2 x \right )\right ) \sin \left (2 x \right )}{8}+\frac {\ln \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 48
DSolve[y''[x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} (-\operatorname {CosIntegral}(2 x) \cos (2 x)-\text {Si}(2 x) \sin (2 x)+\log (x)+4 c_1 \cos (2 x)+4 c_2 \sin (2 x)) \]