29.25.19 problem 716

Internal problem ID [5306]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 716
Date solved : Monday, January 27, 2025 at 11:08:09 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 37

dsolve(x*(x^3+y(x)^5)*diff(y(x),x) = (x^3-y(x)^5)*y(x),y(x), singsol=all)
 

\[ \ln \left (x \right )-c_{1} +\frac {5 \ln \left (\frac {4 y \left (x \right )^{5}-x^{3}}{x^{3}}\right )}{8}-\frac {5 \ln \left (\frac {y \left (x \right )}{x^{{3}/{5}}}\right )}{2} = 0 \]

✓ Solution by Mathematica

Time used: 1.861 (sec). Leaf size: 141

DSolve[x(x^3+y[x]^5)D[y[x],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*}