81.1.32 problem 2-30
Internal
problem
ID
[21477]
Book
:
The
Differential
Equations
Problem
Solver.
VOL.
I.
M.
Fogiel
director.
REA,
NY.
1978.
ISBN
78-63609
Section
:
Chapter
2.
Separable
differential
equations
Problem
number
:
2-30
Date
solved
:
Thursday, October 02, 2025 at 07:39:44 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} x +2 y-4-\left (2 x +y-5\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.135 (sec). Leaf size: 116
ode:=x+2*y(x)-4-(2*x+y(x)-5)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x -2\right )^{2}-1}-27 c_1 \left (x -2\right )\right )^{{2}/{3}}}{6}+\frac {i \sqrt {3}}{2}+\left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x -2\right )^{2}-1}-27 c_1 x +54 c_1 \right )^{{1}/{3}} \left (x -1\right ) c_1}{\left (3 \sqrt {3}\, \sqrt {27 c_1^{2} \left (x -2\right )^{2}-1}-27 c_1 \left (x -2\right )\right )^{{1}/{3}} c_1}
\]
✓ Mathematica. Time used: 0.038 (sec). Leaf size: 70
ode=(x+2*y[x]-4)-(2*x-y[x]-5)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [32 \arctan \left (\frac {-2 y(x)-x+4}{y(x)-2 x+5}\right )=8 \log \left (\frac {5 x^2+5 y(x)^2-6 y(x)-28 x+41}{(5 x-14)^2}\right )+16 \log (5 x-14)+5 c_1,y(x)\right ]
\]
✓ Sympy. Time used: 100.244 (sec). Leaf size: 371
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)
\[
\left [ y{\left (x \right )} = \frac {\frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}} + \sqrt {3} x - i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}}{3} + \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}}{3} - \sqrt {3} + i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {- \frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}} + \sqrt {3} x + i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}}{3} - \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}}{3} - \sqrt {3} - i}{\sqrt {3} + i}, \ y{\left (x \right )} = \frac {3^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}} + x - \frac {\sqrt [3]{3} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 108 x + 108} - 18\right )}}{3} - 1\right ]
\]