Internal problem ID [3454]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 716.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (x^{3}+y^{5}\right ) y^{\prime }-\left (x^{3}-y^{5}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve(x*(x^3+y(x)^5)*diff(y(x),x) = (x^3-y(x)^5)*y(x),y(x), singsol=all)
\[ \ln \relax (x )-c_{1}-\frac {5 \ln \left (\frac {y \relax (x )}{x^{\frac {3}{5}}}\right )}{2}+\frac {5 \ln \left (-\frac {-4 y \relax (x )^{5}+x^{3}}{x^{3}}\right )}{8} = 0 \]
✓ Solution by Mathematica
Time used: 1.651 (sec). Leaf size: 141
DSolve[x(x^3+y[x]^5)y'[x]==(x^3-y[x]^5)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [4 \text {$\#$1}^5 x-4 \text {$\#$1}^4 c_1-x^4\&,1\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5 x-4 \text {$\#$1}^4 c_1-x^4\&,2\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5 x-4 \text {$\#$1}^4 c_1-x^4\&,3\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5 x-4 \text {$\#$1}^4 c_1-x^4\&,4\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5 x-4 \text {$\#$1}^4 c_1-x^4\&,5\right ] \\ \end{align*}