Internal problem ID [2167]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=12 \cos \left (x \right )^{2}} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0, y^{\prime }\left (\frac {\pi }{2}\right ) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)+4*y(x)=12*cos(x)^2,y(1/2*Pi) = 0, D(y)(1/2*Pi) = 1/2*Pi],y(x), singsol=all)
\[ y = \frac {\left (3 x -2 \pi \right ) \sin \left (2 x \right )}{2}+\frac {3 \cos \left (2 x \right )}{2}+\frac {3}{2} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 23
DSolve[{y''[x]+4*y[x]==12*Cos[x]^2,{y[Pi/2]==0,y'[Pi/2]==Pi/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x) ((3 x-2 \pi ) \sin (x)+3 \cos (x)) \]