87.4.13 problem 13

Internal problem ID [23279]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:28:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }-7 y&=6 x \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 55

ode:=y(x)*diff(y(x),x)-7*y(x) = 6*x; 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {\ln \left (\frac {-6 x^{2}-7 x y+y^{2}}{x^{2}}\right )}{2}+\frac {7 \sqrt {73}\, \operatorname {arctanh}\left (\frac {\left (2 y-7 x \right ) \sqrt {73}}{73 x}\right )}{73}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 68

ode=y[x]*D[y[x],x]-7*y[x]==6*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{146} \left (73+7 \sqrt {73}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {73}+7\right )+\frac {1}{146} \left (73-7 \sqrt {73}\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {73}-7\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + y(x)*Derivative(y(x), x) - 7*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out