Internal problem ID [3585]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 329.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]
\[ \boxed {2 x^{2} y^{\prime }+2 y x -x^{2} y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(2*x^2*diff(y(x),x)+1+2*x*y(x)-x^2*y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )}{x} \]
✓ Solution by Mathematica
Time used: 1.03 (sec). Leaf size: 61
DSolve[2 x^2 y'[x]+1+2 x y[x]- x^2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \tan \left (\frac {1}{2} i \log (x)+c_1\right )}{x} y(x)\to \frac {-x+e^{2 i \text {Interval}[\{0,\pi \}]}}{x^2+x e^{2 i \text {Interval}[\{0,\pi \}]}} \end{align*}