69.15.5 problem 436

Internal problem ID [18243]
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 : 436
Date solved : Thursday, October 02, 2025 at 03:09:45 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6 \\ y^{\prime }\left (0\right )&=10 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+3*y(x) = 0; 
ic:=[y(0) = 6, D(y)(0) = 10]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 17

ode=D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==0; 
ic={y[0]==6,Derivative[1][y][0] ==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^x \left (e^{2 x}+2\right ) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (2 e^{2 x} + 4\right ) e^{x} \]