29.26.7 problem 743

Internal problem ID [5328]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 743
Date solved : Monday, January 27, 2025 at 11:14:45 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.235 (sec). Leaf size: 18

dsolve(x*(x-y(x)*tan(y(x)/x))*diff(y(x),x)+(x+y(x)*tan(y(x)/x))*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 31

DSolve[x(x-y[x]*Tan[y[x]/x])*D[y[x],x]+(x+y[x]*Tan[y[x]/x])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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