Internal problem ID [1961]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}=-\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((x/y(x)*cos(x/y(x))+sin(x/y(x))+cos(x) )-x^2/y(x)^2*cos(x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {x}{\arcsin \left (\frac {\sin \left (x \right )+c_{1}}{x}\right )} \]
✓ Solution by Mathematica
Time used: 25.647 (sec). Leaf size: 25
DSolve[(x/y[x]*Cos[x/y[x]]+Sin[x/y[x]]+Cos[x] )-x^2/y[x]^2*Cos[x/y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\arcsin \left (\frac {\sin (x)+c_1}{x}\right )} y(x)\to 0 \end{align*}