29.18.16 problem 492

Internal problem ID [5090]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 492
Date solved : Sunday, March 30, 2025 at 06:37:01 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \end{align*}

✓ Maple. Time used: 1.682 (sec). Leaf size: 31

ode:=(5-x+6*y(x))*diff(y(x),x) = 3-x+4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {9+\left (-8 x -8\right ) c_1}-3+\left (4 x -4\right ) c_1}{8 c_1} \]

✓ Mathematica. Time used: 60.169 (sec). Leaf size: 1177

ode=(5-x+6 y[x])D[y[x],x]==3-x+4 y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 2.583 (sec). Leaf size: 58

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (-x + 6*y(x) + 5)*Derivative(y(x), x) - 4*y(x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {3 C_{1}}{8} + \frac {x}{2} + \frac {\sqrt {C_{1} \left (9 C_{1} - 8 x - 8\right )}}{8} - \frac {1}{2}, \ y{\left (x \right )} = - \frac {3 C_{1}}{8} + \frac {x}{2} - \frac {\sqrt {C_{1} \left (9 C_{1} - 8 x - 8\right )}}{8} - \frac {1}{2}\right ] \]