Internal problem ID [15457]
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: 713.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (\pi \right ) = {\mathrm e}^{\pi }] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=0,y(0) = 0, D(y)(Pi) = exp(Pi)],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{x} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 12
DSolve[{y''[x]-2*y'[x]+2*y[x]==0,{y[0]==0,y'[Pi]==Exp[Pi]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^x \sin (x) \]