10.5.24 problem 30
Internal
problem
ID
[1216]
Book
:
Elementary
differential
equations
and
boundary
value
problems,
10th
ed.,
Boyce
and
DiPrima
Section
:
Section
2.6.
Page
100
Problem
number
:
30
Date
solved
:
Saturday, March 29, 2025 at 10:47:45 PM
CAS
classification
:
[_rational]
\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.004 (sec). Leaf size: 322
ode:=3*x+6/y(x)+(x^2/y(x)+3*y(x)/x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {-12 x^{3}+\left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{2}/{3}}}{6 \left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{1}/{3}}} \\
y &= -\frac {\left (1+i \sqrt {3}\right ) \left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{1}/{3}}}{12}-\frac {x^{3} \left (i \sqrt {3}-1\right )}{\left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{1}/{3}}} \\
y &= \frac {12 i \sqrt {3}\, x^{3}+i \sqrt {3}\, \left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{2}/{3}}+12 x^{3}-\left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{2}/{3}}}{12 \left (-324 x^{2}-108 c_1 +12 \sqrt {12 x^{9}+729 x^{4}+486 c_1 \,x^{2}+81 c_1^{2}}\right )^{{1}/{3}}} \\
\end{align*}
✓ Mathematica. Time used: 4.808 (sec). Leaf size: 331
ode=3*x+6/y[x]+(x^2/y[x]+3*y[x]/x)*D[y[x],x] == 0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {\sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{3 \sqrt [3]{2}}-\frac {\sqrt [3]{2} x^3}{\sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}} \\
y(x)\to \frac {\left (-1+i \sqrt {3}\right ) \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{6 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) x^3}{2^{2/3} \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}} \\
y(x)\to \frac {\left (1-i \sqrt {3}\right ) x^3}{2^{2/3} \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-81 x^2+\sqrt {108 x^9+729 \left (-3 x^2+c_1\right ){}^2}+27 c_1}}{6 \sqrt [3]{2}} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(3*x + (x**2/y(x) + 3*y(x)/x)*Derivative(y(x), x) + 6/y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out