Internal problem ID [12207]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 157.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=2 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*y(x)=2*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (2 x \right )+c_{1} \cos \left (2 x \right )-\frac {x \cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==2*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} ((1+8 c_2) \sin (2 x)-4 (x-2 c_1) \cos (2 x)) \]