64.6.5 problem 5

Internal problem ID [13284]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:45:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.085 (sec). Leaf size: 47

ode:=3*x-5*y(x)+(x+y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {6 c_1 x -\sqrt {8 c_1 x +1}+1}{2 c_1} \\ y &= \frac {6 c_1 x +1+\sqrt {8 c_1 x +1}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 40

ode=(3*x-5*y[x])+(x+y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]+1}{(K[1]-3) (K[1]-1)}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.102 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x + (x + y(x))*Derivative(y(x), x) - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{2} + 3 x - \frac {\sqrt {C_{1} \left (C_{1} + 8 x\right )}}{2}, \ y{\left (x \right )} = \frac {C_{1}}{2} + 3 x + \frac {\sqrt {C_{1} \left (C_{1} + 8 x\right )}}{2}\right ] \]