Internal problem ID [14329]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {-y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.313 (sec). Leaf size: 25
dsolve([(-2*x-y(x)*cos(x*y(x)))+(2*y(x)-x*cos(x*y(x)))*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-x^{4}-\sin \left (\textit {\_Z} \right ) x^{2}+\textit {\_Z}^{2}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.234 (sec). Leaf size: 20
DSolve[{(-2*x-y[x]*Cos[x*y[x]])+(2*y[x]-x*Cos[x*y[x]])*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2-y(x)^2+\sin (x y(x))=0,y(x)\right ] \]