Internal problem ID [6327]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-2 y+b y^{2}-c \,x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 31
dsolve(x*diff(y(x),x)-2*y(x)+b*y(x)^2=c*x^4,y(x), singsol=all)
\[ y \relax (x ) = \frac {i \tan \left (-\frac {i \sqrt {b}\, x^{2} \sqrt {c}}{2}+c_{1}\right ) x^{2} \sqrt {c}}{\sqrt {b}} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 145
DSolve[x*y'[x]-2*y[x]+b*y[x]^2==c*x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {c} x^2 \left (-\cosh \left (\frac {1}{2} \sqrt {b} \sqrt {c} x^2\right )+c_1 \sin \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )\right )}{\sqrt {-b} \left (\sin \left (\frac {1}{2} \sqrt {-b} \sqrt {c} x^2\right )+c_1 \cosh \left (\frac {1}{2} \sqrt {b} \sqrt {c} x^2\right )\right )} \\ y(x)\to \frac {\sqrt {c} x^2 \tanh \left (\frac {1}{2} \sqrt {b} \sqrt {c} x^2\right )}{\sqrt {b}} \\ \end{align*}