15.4.18 problem 19

Internal problem ID [2931]
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
Date solved : Monday, January 27, 2025 at 06:57:58 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.038 (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)
 

\[ y = \frac {\operatorname {RootOf}\left (-8 \cos \left (\textit {\_Z} \right ) x^{4}+4 c_1 \,x^{4}+\textit {\_Z}^{4}\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 22

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

\[ \text {Solve}\left [\frac {y(x)^4}{4}-2 \cos (x y(x))=c_1,y(x)\right ] \]