Internal problem ID [15369]
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: 600.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=2 \,{\mathrm e}^{x} x^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=2*x^2*exp(x),y(0) = 2, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \left (\cos \left (x \right )-2 \sin \left (x \right )\right ) {\mathrm e}^{2 x}+\left (1+x \right )^{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 28
DSolve[{y''[x]-4*y'[x]+5*y[x]==2*x^2*Exp[x],{y[0]==2,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left ((x+1)^2-2 e^x \sin (x)+e^x \cos (x)\right ) \]