Internal problem ID [5971]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 4(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\omega ^{2} y=A \cos \left (\omega x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+omega^2*y(x)=A*cos(omega*x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (\omega x \right ) \left (A x +2\right )}{2 \omega } \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 21
DSolve[{y''[x]+\[Omega]^2*y[x]==A*Cos[\[Omega]*x],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(A x+2) \sin (x \omega )}{2 \omega } \]