85.38.3 problem 3

Internal problem ID [22755]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 175
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:14:22 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-(m__1+m__2)*diff(y(x),x)+m__1*m__2*y(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {-{\mathrm e}^{m_{2} x}+{\mathrm e}^{m_{1} x}}{m_{1} -m_{2}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-(m1+m2)*D[y[x],x]+m1*m2*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{\text {m1} x}-e^{\text {m2} x}}{\text {m1}-\text {m2}} \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
m1 = symbols("m1") 
m2 = symbols("m2") 
y = Function("y") 
ode = Eq(m1*m2*y(x) - (m1 + m2)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{m_{1} x}}{m_{1} - m_{2}} - \frac {e^{m_{2} x}}{m_{1} - m_{2}} \]