15.3.20 problem 20

Internal problem ID [2913]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 20
Date solved : Sunday, March 30, 2025 at 12:53:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y+\left (4 x -2 y+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=0 \end{align*}

✗ Maple

ode:=2*x+y(x)+(4*x-2*y(x)+1)*diff(y(x),x) = 0; 
ic:=y(1/2) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 128

ode=(2*x+y[x])+(4*x-2*y[x]+1)*D[y[x],x]==0; 
ic={y[1/2]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {9}{656} \left (6 \sqrt {41} \text {arctanh}\left (\frac {-\frac {2 (8 x+1)}{-2 y(x)+4 x+1}-3}{\sqrt {41}}\right )+41 \left (\log \left (\frac {2 \left (16 x^2-16 y(x)^2+(40 x+13) y(x)-6 x-2\right )}{(8 x+1)^2}\right )+2 \log (8 x+1)\right )\right )=\frac {1}{656} \left (-9 \left (6 \sqrt {41} \text {arctanh}\left (\frac {19}{3 \sqrt {41}}\right )-82 \log (5)+41 \log \left (\frac {25}{2}\right )\right )+369 i \pi \right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (4*x - 2*y(x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {y(1/2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out