29.17.6 problem 465

Internal problem ID [5063]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 465
Date solved : Sunday, March 30, 2025 at 06:34:29 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.172 (sec). Leaf size: 33

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

\[ y = \frac {-\sqrt {4-27 \left (x +\frac {1}{3}\right )^{2} c_1^{2}}+\left (3 x +3\right ) c_1}{6 c_1} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 67

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

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

✓ Sympy. Time used: 2.447 (sec). Leaf size: 48

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

\[ \left [ y{\left (x \right )} = \frac {x}{2} - \frac {\sqrt {C_{1} - 27 x^{2} - 18 x}}{6} + \frac {1}{2}, \ y{\left (x \right )} = \frac {x}{2} + \frac {\sqrt {C_{1} - 27 x^{2} - 18 x}}{6} + \frac {1}{2}\right ] \]