Internal problem ID [15362]
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: 593.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=2 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=2*exp(2*x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 14
DSolve[{y''[x]-4*y'[x]+4*y[x]==2*Exp[2*x],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} x^2 \]