Internal problem ID [2001]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {2 y-\left (y^{4}+x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(2*y(x)=(y(x)^4+x)*diff(y(x),x),y(x), singsol=all)
\[ x -\frac {y^{4}}{7}-\sqrt {y}\, c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.102 (sec). Leaf size: 257
DSolve[2*y[x]==(y[x]^4+x)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,1\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,2\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,3\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,4\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,5\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,6\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,7\right ] y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,8\right ] \end{align*}