15.7.20 problem 20

Internal problem ID [3001]
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
Date solved : Monday, January 27, 2025 at 07:07:08 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.911 (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)
 

\[ y = \frac {100 x^{2}}{\operatorname {RootOf}\left (\textit {\_Z}^{9}-100000000 x^{9}-9 \textit {\_Z}^{8}\right )^{2}} \]

✓ Solution by Mathematica

Time used: 4.762 (sec). Leaf size: 33

DSolve[{2*y[x]==(x^2*y[x]^4+x)*D[y[x],x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {Root}\left [\text {$\#$1}^9 x^2+18 \text {$\#$1}^5 x+81 \text {$\#$1}-100 x^2\&,1\right ] \]