Internal problem ID [15460]
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 17. Boundary value problems. Exercises page
163
Problem number: 716.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (\pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)+y(x)=1,y(0) = 0, D(y)(Pi) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 1-\cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 11
DSolve[{y''[x]+y[x]==1,{y[0]==0,y'[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 1-\cos (x) \]