Internal problem ID [12127]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right )-y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve(x*cos(y(x)/x)*(y(x)+x*diff(y(x),x))=y(x)*sin(y(x)/x)*(x*diff(y(x),x)-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{\cos \left (\operatorname {RootOf}\left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_{1} \right )\right ) x} \]
✓ Solution by Mathematica
Time used: 0.569 (sec). Leaf size: 31
DSolve[x*Cos[y[x]/x]*(y[x]+x*y'[x])==y[x]*Sin[y[x]/x]*(x*y'[x]-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\log \left (\frac {y(x)}{x}\right )-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=2 \log (x)+c_1,y(x)\right ] \]