23.3.96 problem 98

Internal problem ID [5810]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 98
Date solved : Tuesday, September 30, 2025 at 02:03:36 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

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

\[ y = \left (c_1 \,{\mathrm e}^{2 x \sqrt {a^{2}-b^{2}}}+c_2 \right ) {\mathrm e}^{-\left (a +\sqrt {a^{2}-b^{2}}\right ) x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to e^{-\left (x \left (\sqrt {a^2-b^2}+a\right )\right )} \left (c_2 e^{2 x \sqrt {a^2-b^2}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 36

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

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