Internal problem ID [2325]
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 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y x -\sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 49
dsolve(diff(y(x),x$2)+x*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {AiryAi}\left (-x \right ) c_{2} +\operatorname {AiryBi}\left (-x \right ) c_{1} +\pi \left (\operatorname {AiryAi}\left (-x \right ) \left (\int \operatorname {AiryBi}\left (-x \right ) \sin \left (x \right )d x \right )-\operatorname {AiryBi}\left (-x \right ) \left (\int \operatorname {AiryAi}\left (-x \right ) \sin \left (x \right )d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 51.516 (sec). Leaf size: 99
DSolve[y''[x]+x*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \operatorname {AiryAi}\left (\sqrt [3]{-1} x\right ) \int _1^x(-1)^{2/3} \pi \operatorname {AiryBi}\left (\sqrt [3]{-1} K[1]\right ) \sin (K[1])dK[1]+\operatorname {AiryBi}\left (\sqrt [3]{-1} x\right ) \int _1^x-(-1)^{2/3} \pi \operatorname {AiryAi}\left (\sqrt [3]{-1} K[2]\right ) \sin (K[2])dK[2]+c_1 \operatorname {AiryAi}\left (\sqrt [3]{-1} x\right )+c_2 \operatorname {AiryBi}\left (\sqrt [3]{-1} x\right ) \\ \end{align*}