29.30.23 problem 883
Internal
problem
ID
[5463]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
30
Problem
number
:
883
Date
solved
:
Tuesday, March 04, 2025 at 09:40:10 PM
CAS
classification
:
[_rational, _dAlembert]
\begin{align*} \left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \end{align*}
✓ Maple. Time used: 0.053 (sec). Leaf size: 249
ode:=(5+3*x)*diff(y(x),x)^2-(3+3*y(x))*diff(y(x),x)+y(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {-108 \left (x -\frac {3 y \left (x \right )}{2}-\frac {\sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{2}+\frac {1}{6}\right ) \left (c_{1} -\frac {\operatorname {Ei}_{1}\left (\frac {-9-9 y \left (x \right )-3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{6 x +10}\right )}{2}\right ) {\mathrm e}^{\frac {-9-9 y \left (x \right )-3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{6 x +10}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\
\frac {108 \left (c_{1} +\frac {\operatorname {Ei}_{1}\left (\frac {-9-9 y \left (x \right )+3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{6 x +10}\right )}{2}\right ) \left (x -\frac {3 y \left (x \right )}{2}+\frac {\sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{2}+\frac {1}{6}\right ) {\mathrm e}^{\frac {-9-9 y \left (x \right )+3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{6 x +10}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 1.828 (sec). Leaf size: 106
ode=(5+3 x) (D[y[x],x])^2-(3+3 y[x])D[y[x],x]+y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=\frac {e^{-3 K[1]} (3 K[1]-1) \left ((9-27 K[1]) \operatorname {ExpIntegralEi}(3 K[1])+4 e^{3 K[1]}\right )}{9 K[1]-3}+c_1 e^{-3 K[1]} (3 K[1]-1),y(x)=\frac {3 x K[1]^2}{3 K[1]-1}+\frac {5 K[1]^2-3 K[1]}{3 K[1]-1}\right \},\{y(x),K[1]\}\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((3*x + 5)*Derivative(y(x), x)**2 - (3*y(x) + 3)*Derivative(y(x), x) + y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out