29.23.8 problem 639
Internal
problem
ID
[5230]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
23
Problem
number
:
639
Date
solved
:
Monday, January 27, 2025 at 10:37:02 AM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.105 (sec). Leaf size: 35
dsolve(x*(3*x-y(x)^2)*diff(y(x),x)+(5*x-2*y(x)^2)*y(x) = 0,y(x), singsol=all)
\[
\ln \left (x \right )-c_{1} -\frac {2 \ln \left (\frac {5 y \left (x \right )^{2}-13 x}{x}\right )}{65}+\frac {6 \ln \left (\frac {y \left (x \right )}{\sqrt {x}}\right )}{13} = 0
\]
✓ Solution by Mathematica
Time used: 6.502 (sec). Leaf size: 661
DSolve[x(3 x-y[x]^2)D[y[x],x]+(5 x-2 y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,1\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,2\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,3\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,4\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,5\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,6\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,7\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,8\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,9\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,10\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,11\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,12\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,13\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,14\right ] \\
y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,15\right ] \\
\end{align*}