49.23.2 problem 1(b)

Internal problem ID [7760]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 1(b)
Date solved : Wednesday, March 05, 2025 at 04:54:47 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = -c_{1} \operatorname {Ei}_{1}\left ({\mathrm e}^{x}\right )+x +c_{2} \]

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 18

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

\[ y(x)\to c_1 \operatorname {ExpIntegralEi}\left (-e^x\right )+x+c_2 \]

✓ Sympy. Time used: 1.204 (sec). Leaf size: 17

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

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