84.20.3 problem 12.11

Internal problem ID [22219]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 12. Second order linear homogeneous differential equations with constant coefficients. Supplementary problems
Problem number : 12.11
Date solved : Thursday, October 02, 2025 at 08:36:22 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to e^x (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 10

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

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