Internal problem ID [3586]
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]
\[ \boxed {2 x^{2} y^{\prime }-2 y x -\left (-x \cot \left (x \right )+1\right ) \left (x^{2}-y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\tanh \left (\frac {\ln \left (\sin \left (x \right )\right )}{2}-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right ) x \]
✓ Solution by Mathematica
Time used: 1.1 (sec). Leaf size: 44
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 \frac {x \left (x-e^{2 c_1} \sin (x)\right )}{x+e^{2 c_1} \sin (x)} y(x)\to -x y(x)\to x \end{align*}