29.25.18 problem 715

Internal problem ID [5305]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 715
Date solved : Monday, January 27, 2025 at 11:08:04 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{2}-y^{5}\right ) y^{\prime }&=2 y x \end{align*}

✓ Solution by Maple

Time used: 0.116 (sec). Leaf size: 25

dsolve((x^2-y(x)^5)*diff(y(x),x) = 2*x*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (x^{8} \textit {\_Z}^{5}+4-{\mathrm e}^{\frac {8 c_{1}}{5}} \textit {\_Z} \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 2.041 (sec). Leaf size: 121

DSolve[(x^2-y[x]^5)D[y[x],x]==2 x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,5\right ] \\ y(x)\to 0 \\ \end{align*}