29.17.10 problem 469

Internal problem ID [5067]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 469
Date solved : Tuesday, March 04, 2025 at 07:50:43 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \end{align*}

✓ Maple. Time used: 0.696 (sec). Leaf size: 33

ode:=(3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 67

ode=(3+2 x-2 y[x])D[y[x],x]==1+6 x-2 y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ y(x)\to \frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ \end{align*}

✓ Sympy. Time used: 2.493 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + (2*x - 2*y(x) + 3)*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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