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
:
Monday, January 27, 2025 at 11:24:46 AM
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*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 249
dsolve((5+3*x)*diff(y(x),x)^2-(3+3*y(x))*diff(y(x),x)+y(x) = 0,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*}
✓ Solution by Mathematica
Time used: 1.828 (sec). Leaf size: 106
DSolve[(5+3 x) (D[y[x],x])^2-(3+3 y[x])D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\left \{x=\frac {e^{-3 K[1]} (3 K[1]-1) \left ((9-27 K[1]) \operatorname {ExpIntegralEi}(3 K[1])+4 e^{3 K[1]}\right )}{9 K[1]-3}+c_1 e^{-3 K[1]} (3 K[1]-1),y(x)=\frac {3 x K[1]^2}{3 K[1]-1}+\frac {5 K[1]^2-3 K[1]}{3 K[1]-1}\right \},\{y(x),K[1]\}\right ]
\]