Internal problem ID [1960]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {2 y \sin \left (x y\right )+\left (2 x \sin \left (x y\right )+y^{3}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(2*y(x)*sin(x*y(x))+(2*x*sin(x*y(x))+y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-8 \cos \left (\textit {\_Z} \right ) x^{4}+4 c_{1} x^{4}+\textit {\_Z}^{4}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 22
DSolve[2*y[x]*Sin[x*y[x]]+(2*x*Sin[x*y[x]]+y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^4}{4}-2 \cos (x y(x))=c_1,y(x)\right ] \]