75.18.4 problem 593

Internal problem ID [17021]
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 : Monday, March 31, 2025 at 03:38:20 PM
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*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+4*y(x) = 2*exp(2*x); 
ic:=y(0) = 0, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.208 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 2*exp(2*x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} e^{2 x} \]