12.6.12 problem 12

Internal problem ID [1691]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:28:05 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

dsolve((y(x)*sin(x*y(x))+x*y(x)^2*cos(x*y(x)))+(x*sin(x*y(x))+x*y(x)^2*cos(x*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved