88.10.1 problem 1

Internal problem ID [24036]
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 2. Differential equations of first order. Exercise at page 52
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:55:01 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=(2*x+1)*diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \sqrt {x +\frac {1}{2}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to c_2-c_1 \sqrt {-2 x-1} \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 14

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

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