29.16.7 problem 450

Internal problem ID [5048]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 450
Date solved : Tuesday, March 04, 2025 at 07:46:39 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \end{align*}

✓ Maple. Time used: 0.700 (sec). Leaf size: 32

ode:=(5-2*x-y(x))*diff(y(x),x)+4-x-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {-\sqrt {3 \left (x -2\right )^{2} c_{1}^{2}+1}+\left (-2 x +5\right ) c_{1}}{c_{1}} \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 53

ode=(5-2 x-y[x])D[y[x],x]+4-x-2 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {3 x^2-12 x+25+c_1}-2 x+5 \\ y(x)\to \sqrt {3 x^2-12 x+25+c_1}-2 x+5 \\ \end{align*}

✓ Sympy. Time used: 1.933 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (-2*x - y(x) + 5)*Derivative(y(x), x) - 2*y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 2 x - \sqrt {C_{1} + 3 x^{2} - 12 x} + 5, \ y{\left (x \right )} = - 2 x + \sqrt {C_{1} + 3 x^{2} - 12 x} + 5\right ] \]