Internal problem ID [2206]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+2*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right ) c_{1} +\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 30
DSolve[y''[x]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x)+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \]