Internal problem ID [8435]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 98.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x y^{\prime }+a y^{2}-b y=-c \,x^{2 b}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(x*diff(y(x),x) + a*y(x)^2 - b*y(x) + c*x^(2*b)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\tan \left (\frac {x^{b} \sqrt {a}\, \sqrt {c}+c_{1} b}{b}\right ) \sqrt {c}\, x^{b}}{\sqrt {a}} \]
✓ Solution by Mathematica
Time used: 0.356 (sec). Leaf size: 211
DSolve[x*y'[x] + a*y[x]^2 - b*y[x] + c*x^(2*b)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {-c} x^b \left (-\cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )+c_1 \sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )\right )}{\sqrt {-a} \left (\sin \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )+c_1 \cos \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )\right )} \\ y(x)\to \frac {\sqrt {-c} x^b \tan \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {-a}} \\ y(x)\to \frac {\sqrt {-c} x^b \tan \left (\frac {\sqrt {-a} \sqrt {-c} x^b}{b}\right )}{\sqrt {-a}} \\ \end{align*}