9.3.10 problem 10
Internal
problem
ID
[2903]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
7,
page
28
Problem
number
:
10
Date
solved
:
Tuesday, September 30, 2025 at 06:01:54 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} x +2 y+2&=\left (2 x +y-1\right ) y^{\prime } \end{align*}
✓ Maple. Time used: 0.232 (sec). Leaf size: 116
ode:=x+2*y(x)+2 = (2*x+y(x)-1)*diff(y(x),x);
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\frac {1}{6}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \sqrt {3}\, \sqrt {-1+243 \left (x -\frac {4}{3}\right )^{2} c_1^{2}}+\left (-81 x +108\right ) c_1 \right )^{{2}/{3}}}{18}+\frac {i \sqrt {3}}{6}+\left (3 \sqrt {3}\, \sqrt {-1+243 \left (x -\frac {4}{3}\right )^{2} c_1^{2}}-81 c_1 x +108 c_1 \right )^{{1}/{3}} \left (x -3\right ) c_1}{\left (3 \sqrt {3}\, \sqrt {-1+243 \left (x -\frac {4}{3}\right )^{2} c_1^{2}}+\left (-81 x +108\right ) c_1 \right )^{{1}/{3}} c_1}
\]
✓ Mathematica. Time used: 60.119 (sec). Leaf size: 1687
ode=(x+2*y[x]+2)==(2*x+y[x]-1)*D[y[x],x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✓ Sympy. Time used: 105.669 (sec). Leaf size: 377
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x - (2*x + y(x) - 1)*Derivative(y(x), x) + 2*y(x) + 2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}} + \sqrt {3} x - i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}}{3} + \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}}{3} - 3 \sqrt {3} + 3 i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {- \frac {2 \cdot 3^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}} + \sqrt {3} x + i x + \frac {3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}}{3} - \frac {\sqrt [3]{3} i \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}}{3} - 3 \sqrt {3} - 3 i}{\sqrt {3} + i}, \ y{\left (x \right )} = \frac {3^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}} + x - \frac {\sqrt [3]{3} \sqrt [3]{C_{1} \left (9 x + \sqrt {3} \sqrt {C_{1} + 27 x^{2} - 72 x + 48} - 12\right )}}{3} - 3\right ]
\]