Internal problem ID [3078]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 330.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {2 y^{\prime } x^{2}-2 y x -\left (-x \cot \relax (x )+1\right ) \left (x^{2}-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 21
dsolve(2*x^2*diff(y(x),x) = 2*x*y(x)+(1-x*cot(x))*(x^2-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (-\frac {\ln \relax (x )}{2}+\frac {\ln \left (\sin \relax (x )\right )}{2}+\frac {c_{1}}{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.781 (sec). Leaf size: 37
DSolve[2 x^2 y'[x]==2 x y[x]+(1-x Cot[x])(x^2-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-1+\frac {2 x}{x+e^{2 c_1} \sin (x)}\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}