Internal problem ID [3437]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 699.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
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)
\[ x -\frac {-\frac {y \relax (x )^{5}}{5}+\frac {5 y \relax (x )^{2}}{2}+c_{1}}{y \relax (x ) \left (y \relax (x )^{3}-5\right )^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 47.95 (sec). Leaf size: 342
DSolve[(5 x-y[x]-7 x y[x]^3)y'[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*}