69.1.127 problem 186

Internal problem ID [14280]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 186
Date solved : Tuesday, January 28, 2025 at 06:25:28 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 12

dsolve(x*cos( y(x)/x)*diff(y(x),x)=y(x)*cos( y(x)/x) - x,y(x), singsol=all)
 

\[ y = -\arcsin \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 26

DSolve[x*Cos[ y[x]/x]*D[y[x],x]==y[x]*Cos[ y[x]/x] - x,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\cos (K[1])dK[1]=-\log (x)+c_1,y(x)\right ] \]