Internal problem ID [3455]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 717.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 25
dsolve(x^3*(1+5*x^3*y(x)^7)*diff(y(x),x)+(3*x^5*y(x)^5-1)*y(x)^3 = 0,y(x), singsol=all)
\[ -x^{3} y \relax (x )^{5}-\frac {1}{2 x^{2}}+\frac {1}{2 y \relax (x )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.294 (sec). Leaf size: 253
DSolve[x^3(1+5 x^3 y[x]^7)y'[x]+(3 x^5 y[x]^5-1)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,1\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,2\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,3\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,4\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,5\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,6\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,7\right ] \\ \end{align*}