Internal problem ID [3259]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 515.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } y x +x^{2} \mathrm {arccot}\left (\frac {y}{x}\right )-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\mathrm {arccot}\left (\textit {\_a} \right )}d \textit {\_a} +\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.617 (sec). Leaf size: 31
DSolve[x y[x] y'[x]+x^2 ArcCot[y[x]/x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{\cot ^{-1}(K[1])}dK[1]=-\log (x)+c_1,y(x)\right ] \]