29.19.2 problem 515

Internal problem ID [5111]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 515
Date solved : Monday, January 27, 2025 at 10:11:51 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(x*y(x)*diff(y(x),x)+x^2*arccot(y(x)/x)-y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\operatorname {arccot}\left (\textit {\_a} \right )}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.594 (sec). Leaf size: 31

DSolve[x y[x] D[y[x],x]+x^2 ArcCot[y[x]/x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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