Internal problem ID [2030]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {2 y-\left (x^{2} y^{4}+x \right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.797 (sec). Leaf size: 26
dsolve([2*y(x)=(x^2*y(x)^4+x)*diff(y(x),x),y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {100 x^{2}}{\operatorname {RootOf}\left (\textit {\_Z}^{9}-100000000 x^{9}-9 \textit {\_Z}^{8}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 4.207 (sec). Leaf size: 33
DSolve[{2*y[x]==(x^2*y[x]^4+x)*y'[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {Root}\left [\text {$\#$1}^9 x^2+18 \text {$\#$1}^5 x+81 \text {$\#$1}-100 x^2\&,1\right ] \]