69.1.30 problem 47

Internal problem ID [14183]
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
Date solved : Tuesday, January 28, 2025 at 06:19:32 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.566 (sec). Leaf size: 18

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)
 

\[ y = x \operatorname {RootOf}\left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.322 (sec). Leaf size: 31

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

\[ \text {Solve}\left [-\log \left (\frac {y(x)}{x}\right )-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=2 \log (x)+c_1,y(x)\right ] \]