Internal problem ID [2234]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=x \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+4*y(x)=x*sin(x),y(x), singsol=all)
\[ y = c_{2} \sin \left (2 x \right )+\cos \left (2 x \right ) c_{1} -\frac {2 \cos \left (x \right )}{9}+\frac {x \sin \left (x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} x \sin (x)+c_1 \cos (2 x)+\cos (x) \left (-\frac {2}{9}+2 c_2 \sin (x)\right ) \]