75.13.7 problem 324

Internal problem ID [16841]
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 13. Basic concepts and definitions. Exercises page 98
Problem number : 324
Date solved : Monday, March 31, 2025 at 03:23:59 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 +1 \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 21

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

\[ y(x)\to c_1 e^x+c_2 e^{2 x}+1 \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + 1 \]