83.45.6 problem Ex 6 page 54
Internal
problem
ID
[19470]
Book
:
A
Text
book
for
differentional
equations
for
postgraduate
students
by
Ray
and
Chaturvedi.
First
edition,
1958.
BHASKAR
press.
INDIA
Section
:
Book
Solved
Excercises.
Chapter
IV.
Equations
of
the
first
order
but
not
of
the
first
degree
Problem
number
:
Ex
6
page
54
Date
solved
:
Thursday, March 13, 2025 at 02:32:22 PM
CAS
classification
:
[_dAlembert]
\begin{align*} y&=\frac {x}{y^{\prime }}-a y^{\prime } \end{align*}
✓ Maple. Time used: 0.042 (sec). Leaf size: 396
ode:=y(x) = x/diff(y(x),x)-a*diff(y(x),x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {c_{1} \left (y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}\right )}{\sqrt {\frac {-y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}+2 a}{a}}\, \sqrt {\frac {-2 a -y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}}{a}}}+x +\frac {\left (y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}\right ) \left (3 \ln \left (2\right )-2 \ln \left (\frac {2 \sqrt {\frac {y \left (x \right )^{2}-y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}-2 a^{2}+2 a x}{a^{2}}}\, a -\sqrt {2}\, \left (y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}\right )}{a}\right )\right ) \sqrt {2}}{4 \sqrt {\frac {y \left (x \right )^{2}-y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}-2 a^{2}+2 a x}{a^{2}}}} &= 0 \\
\frac {c_{1} \left (y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}\right )}{2 \sqrt {\frac {-y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}+2 a}{a}}\, \sqrt {\frac {-2 a -y \left (x \right )-\sqrt {4 a x +y \left (x \right )^{2}}}{a}}}+x -\frac {\left (y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}\right ) \sqrt {2}\, \left (-\frac {3 \ln \left (2\right )}{2}+\ln \left (\frac {2 \sqrt {\frac {y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}-2 a^{2}+2 a x +y \left (x \right )^{2}}{a^{2}}}\, a -\left (y \left (x \right )+\sqrt {4 a x +y \left (x \right )^{2}}\right ) \sqrt {2}}{a}\right )\right )}{2 \sqrt {\frac {y \left (x \right ) \sqrt {4 a x +y \left (x \right )^{2}}-2 a^{2}+2 a x +y \left (x \right )^{2}}{a^{2}}}} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 0.765 (sec). Leaf size: 61
ode=y[x]==x/D[y[x],x]-a*D[y[x],x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=\frac {a K[1] \arcsin (K[1])}{\sqrt {1-K[1]^2}}+\frac {c_1 K[1]}{\sqrt {1-K[1]^2}},y(x)=\frac {x}{K[1]}-a K[1]\right \},\{y(x),K[1]\}\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
y = Function("y")
ode = Eq(a*Derivative(y(x), x) - x/Derivative(y(x), x) + y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out