29.23.30 problem 661
Internal
problem
ID
[5252]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
23
Problem
number
:
661
Date
solved
:
Monday, January 27, 2025 at 10:49:46 AM
CAS
classification
:
[[_homogeneous, `class G`], _rational]
\begin{align*} x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \end{align*}
✓ Solution by Maple
Time used: 2.178 (sec). Leaf size: 49
dsolve(x*(3*x-7*y(x)^2)*diff(y(x),x)+(5*x-3*y(x)^2)*y(x) = 0,y(x), singsol=all)
\begin{align*}
y \left (x \right ) &= \operatorname {RootOf}\left (x^{{3}/{2}} \textit {\_Z}^{7}-x^{{5}/{2}} \textit {\_Z}^{3}-c_{1} \right )^{2} \\
y \left (x \right ) &= \operatorname {RootOf}\left (x^{{3}/{2}} \textit {\_Z}^{7}-x^{{5}/{2}} \textit {\_Z}^{3}+c_{1} \right )^{2} \\
\end{align*}
✓ Solution by Mathematica
Time used: 4.497 (sec). Leaf size: 288
DSolve[x(3 x-7 y[x]^2)D[y[x],x]+(5 x-3 y[x]^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,1\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,2\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,3\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,4\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,5\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,6\right ] \\
y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,7\right ] \\
\end{align*}