Internal problem ID [5397]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*y(x)=sin(2*x),y(x), singsol=all)
\[ y = c_{2} \sin \left (2 x \right )+c_{1} \cos \left (2 x \right )-\frac {x \cos \left (2 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{4}+c_1\right ) \cos (2 x)+\frac {1}{8} (1+16 c_2) \sin (x) \cos (x) \]