Internal problem ID [2179]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=2 x -2 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+4*y(x)=2*(x-sin(2*x)),y(x), singsol=all)
\[ y = c_{2} \sin \left (2 x \right )+\cos \left (2 x \right ) c_{1} +\frac {x \left (1+\cos \left (2 x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 30
DSolve[y''[x]+4*y[x]==2*(x-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (x+(x+2 c_1) \cos (2 x)+2 c_2 \sin (2 x)) \]