81.6.3 problem 7-3
Internal
problem
ID
[21549]
Book
:
The
Differential
Equations
Problem
Solver.
VOL.
I.
M.
Fogiel
director.
REA,
NY.
1978.
ISBN
78-63609
Section
:
Chapter
7.
Linear
Differential
Equations.
Page
101.
Problem
number
:
7-3
Date
solved
:
Thursday, October 02, 2025 at 07:47:47 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 2 y-1+\left (3 x -y\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.002 (sec). Leaf size: 21
ode:=2*y(x)-1+(-y(x)+3*x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
x -\frac {y}{5}-\frac {1}{15}-\frac {c_1}{\left (2 y-1\right )^{{3}/{2}}} = 0
\]
✓ Mathematica. Time used: 9.461 (sec). Leaf size: 413
ode=(2*y[x]-1)+(3*x-y[x])*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [72 \text {$\#$1}^5+\text {$\#$1}^4 (-720 x-60)+\text {$\#$1}^3 \left (1800 x^2+840 x-10\right )+\text {$\#$1}^2 \left (-2700 x^2-180 x+15\right )+\text {$\#$1} \left (1350 x^2-90 x\right )-225 x^2+30 x-1+225 c_1{}^2\&,1\right ]\\ y(x)&\to \text {Root}\left [72 \text {$\#$1}^5+\text {$\#$1}^4 (-720 x-60)+\text {$\#$1}^3 \left (1800 x^2+840 x-10\right )+\text {$\#$1}^2 \left (-2700 x^2-180 x+15\right )+\text {$\#$1} \left (1350 x^2-90 x\right )-225 x^2+30 x-1+225 c_1{}^2\&,2\right ]\\ y(x)&\to \text {Root}\left [72 \text {$\#$1}^5+\text {$\#$1}^4 (-720 x-60)+\text {$\#$1}^3 \left (1800 x^2+840 x-10\right )+\text {$\#$1}^2 \left (-2700 x^2-180 x+15\right )+\text {$\#$1} \left (1350 x^2-90 x\right )-225 x^2+30 x-1+225 c_1{}^2\&,3\right ]\\ y(x)&\to \text {Root}\left [72 \text {$\#$1}^5+\text {$\#$1}^4 (-720 x-60)+\text {$\#$1}^3 \left (1800 x^2+840 x-10\right )+\text {$\#$1}^2 \left (-2700 x^2-180 x+15\right )+\text {$\#$1} \left (1350 x^2-90 x\right )-225 x^2+30 x-1+225 c_1{}^2\&,4\right ]\\ y(x)&\to \text {Root}\left [72 \text {$\#$1}^5+\text {$\#$1}^4 (-720 x-60)+\text {$\#$1}^3 \left (1800 x^2+840 x-10\right )+\text {$\#$1}^2 \left (-2700 x^2-180 x+15\right )+\text {$\#$1} \left (1350 x^2-90 x\right )-225 x^2+30 x-1+225 c_1{}^2\&,5\right ]\\ y(x)&\to \frac {1}{2} \end{align*}
✓ Sympy. Time used: 0.784 (sec). Leaf size: 29
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((3*x - y(x))*Derivative(y(x), x) + 2*y(x) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (y{\left (x \right )} - \frac {1}{2} \right )} = C_{1} - \log {\left (\left (\frac {5 \left (x - \frac {1}{6}\right )}{y{\left (x \right )} - \frac {1}{2}} - 1\right )^{\frac {2}{5}} \right )}
\]