29.25.2 problem 699
Internal
problem
ID
[5289]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
25
Problem
number
:
699
Date
solved
:
Monday, January 27, 2025 at 11:04:33 AM
CAS
classification
:
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\begin{align*} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \end{align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 34
dsolve((5*x-y(x)-7*x*y(x)^3)*diff(y(x),x)+5*y(x)-y(x)^4 = 0,y(x), singsol=all)
\[
x +\frac {\frac {y \left (x \right )^{5}}{5}-\frac {5 y \left (x \right )^{2}}{2}-c_{1}}{\left (y \left (x \right )^{3}-5\right )^{2} y \left (x \right )} = 0
\]
✓ Solution by Mathematica
Time used: 47.280 (sec). Leaf size: 342
DSolve[(5 x-y[x]-7 x y[x]^3)D[y[x],x]+5 y[x]-y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,1\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,2\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,3\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,4\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,5\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,6\right ] \\
y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,7\right ] \\
y(x)\to 0 \\
y(x)\to -\sqrt [3]{-5} \\
y(x)\to \sqrt [3]{5} \\
y(x)\to (-1)^{2/3} \sqrt [3]{5} \\
\end{align*}