23.1.485 problem 475

Internal problem ID [5092]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 475
Date solved : Tuesday, September 30, 2025 at 11:35:00 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \end{align*}

✓ Maple. Time used: 1.723 (sec). Leaf size: 31

ode:=(19+9*x+2*y(x))*diff(y(x),x)+18-2*x-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {1+\left (-40 x -120\right ) c_1}-1+\left (4 x +44\right ) c_1}{8 c_1} \]

✓ Mathematica. Time used: 10.148 (sec). Leaf size: 276

ode=(19+9*x+2*y[x])*D[y[x],x]+18-2*x-6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}+(1-i)}-\frac {19}{2}\\ y(x)&\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}}-\frac {19}{2}\\ y(x)&\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}}-\frac {19}{2}\\ y(x)&\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-\frac {19}{2}\\ y(x)&\to -2 (x+1)\\ y(x)&\to \frac {x+11}{2} \end{align*}

✓ Sympy. Time used: 1.675 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (9*x + 2*y(x) + 19)*Derivative(y(x), x) - 6*y(x) + 18,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {x}{2} - \frac {\sqrt {C_{1} \left (C_{1} + 10 x + 30\right )}}{2} + \frac {11}{2}, \ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {x}{2} + \frac {\sqrt {C_{1} \left (C_{1} + 10 x + 30\right )}}{2} + \frac {11}{2}\right ] \]