15.8.34 problem 36

Internal problem ID [3037]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 36
Date solved : Monday, January 27, 2025 at 07:10:59 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 43

dsolve(y(x)*(3*x^2+y(x))-x*(x^2-y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {x^{2} \left (\operatorname {RootOf}\left (\textit {\_Z}^{4} c_{1} -\textit {\_Z} c_{1} +3 x \right )^{3}-1\right )}{3 \operatorname {RootOf}\left (\textit {\_Z}^{4} c_{1} -\textit {\_Z} c_{1} +3 x \right )^{3}} \]

✓ Solution by Mathematica

Time used: 60.143 (sec). Leaf size: 1665

DSolve[y[x]*(3*x^2+y[x])-x*(x^2-y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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