Internal problem ID [15367]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 598.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+4*y(x)=sin(x),y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (2 x \right )}{3}+\cos \left (2 x \right )+\frac {\sin \left (x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 22
DSolve[{y''[x]+4*y[x]==Sin[x],{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} (\sin (x)+\sin (2 x)+3 \cos (2 x)) \]