Internal problem ID [5351]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+9*y(x)=x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {\sin \left (x \right )}{32}+\frac {\cos \left (x \right ) x}{8} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 32
DSolve[y''[x]+9*y[x]==x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{32} (\sin (x)+4 x \cos (x))+c_1 \cos (3 x)+c_2 \sin (3 x) \]