75.18.4 problem 593

Internal problem ID [17092]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 593
Date solved : Tuesday, January 28, 2025 at 09:52:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y = {\mathrm e}^{2 x} x^{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==2*Exp[2*x],{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} x^2 \]