Internal problem ID [15372]
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: 603.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=4 \,{\mathrm e}^{x} \cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (\pi \right ) = \pi \,{\mathrm e}^{\pi }, y^{\prime }\left (\pi \right ) = {\mathrm e}^{\pi }] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=4*exp(x)*cos(x),y(Pi) = Pi*exp(Pi), D(y)(Pi) = exp(Pi)],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (2 x -\pi -1\right ) \sin \left (x \right )-{\mathrm e}^{x} \cos \left (x \right ) \pi \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 24
DSolve[{y''[x]-2*y'[x]+2*y[x]==4*Exp[x]*Cos[x],{y[Pi]==Pi*Exp[Pi],y'[Pi]==Exp[Pi]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^x ((-2 x+\pi +1) \sin (x)+\pi \cos (x)) \]