88.15.9 problem 1

Internal problem ID [24105]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 97
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:59:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x)-(m__1+m__2)*diff(y(x),x)+m__1*m__2*y(x) = exp(m*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{m_{2} x} c_2 +{\mathrm e}^{m_{1} x} c_1 +\frac {{\mathrm e}^{m x}}{\left (m -m_{2} \right ) \left (m -m_{1} \right )} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to \frac {e^{m x}}{(m-\text {m1}) (m-\text {m2})}+c_2 e^{\text {m1} x}+c_1 e^{\text {m2} x} \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 34

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

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