82.3.4 problem Ex. 4

Internal problem ID [18663]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 16
Problem number : Ex. 4
Date solved : Monday, March 31, 2025 at 05:52:32 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y+3 x \right ) y^{\prime }+y-2 x&=0 \end{align*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 55

ode:=(4*y(x)+3*x)*diff(y(x),x)+y(x)-2*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {\ln \left (\frac {-x^{2}+2 x y+2 y^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {3}\, \operatorname {arctanh}\left (\frac {\left (2 y+x \right ) \sqrt {3}}{3 x}\right )}{6}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 63

ode=(4*y[x]+3*x)*D[y[x],x]+y[x]-2*x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (\left (6+\sqrt {3}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {3}-1\right )-\left (\sqrt {3}-6\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {3}+1\right )\right )=-2 \log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (3*x + 4*y(x))*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out