66.1.2 problem Problem 2
Internal
problem
ID
[13778]
Book
:
Differential
equations
and
the
calculus
of
variations
by
L.
ElSGOLTS.
MIR
PUBLISHERS,
MOSCOW,
Third
printing
1977.
Section
:
Chapter
1,
First-Order
Differential
Equations.
Problems
page
88
Problem
number
:
Problem
2
Date
solved
:
Monday, March 31, 2025 at 08:11:23 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.265 (sec). Leaf size: 297
ode:=12*x+6*y(x)-9+(5*x+2*y(x)-3)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {3 \left (\left (x -1\right ) \sqrt {x^{2} \operatorname {RootOf}\left (8 \textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )+20 \textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right ) \left ({\mathrm e}^{-3 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-40 \operatorname {RootOf}\left (8 \textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )+20 \textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right )^{3} x^{3}\right )}+\frac {{\mathrm e}^{-\frac {5 c_1}{2}} \sqrt {2}\, x}{6}\right )}{2 \sqrt {x^{2} \operatorname {RootOf}\left (8 \textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )+20 \textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right ) \left ({\mathrm e}^{-3 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-40 \operatorname {RootOf}\left (8 \textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )+20 \textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right )^{3} x^{3}\right )}}
\]
✓ Mathematica. Time used: 60.061 (sec). Leaf size: 1121
ode=(12*x+6*y[x]-9)+(5*x+2*y[x]-3)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Sympy. Time used: 1.114 (sec). Leaf size: 34
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(12*x + (5*x + 2*y(x) - 3)*Derivative(y(x), x) + 6*y(x) - 9,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (x \right )} = C_{1} - \log {\left (\left (\frac {3}{2} + \frac {y{\left (x \right )} - \frac {3}{2}}{x}\right )^{\frac {2}{5}} \left (4 + \frac {y{\left (x \right )} - \frac {3}{2}}{x}\right )^{\frac {3}{5}} \right )}
\]