75.15.13 problem 444

Internal problem ID [16885]
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 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 444
Date solved : Thursday, March 13, 2025 at 08:58:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+3*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (\sqrt {2}\, \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right )\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-2*D[y[x],x]+3*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (\sqrt {2} \sin \left (\sqrt {2} x\right )+\cos \left (\sqrt {2} x\right )\right ) \]

✓ Sympy. Time used: 0.185 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\sqrt {2} \sin {\left (\sqrt {2} x \right )} + \cos {\left (\sqrt {2} x \right )}\right ) e^{x} \]