2.0 ODE No. 99

ODE No. 99

$a y (x)^{2} - b y (x) - c x^{β} + x y^{'} (x) = 0$ ✓ Mathematica : cpu = 0.180257 (sec), leaf count = 244

DSolve[-(c*x^beta) - b*y[x] + a*y[x]^2 + x*Derivative[1][y][x] == 0,y[x],x]

${{y (x) \to - \frac{\sqrt{- a} \sqrt{c} x^{β / 2} (- 2 J_{\frac{b}{β} - 1} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β}) + c_{1} J_{1 - \frac{b}{β}} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β}) - c_{1} J_{- \frac{b + β}{β}} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β})) - b c_{1} J_{- \frac{b}{β}} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β})}{2 a (J_{\frac{b}{β}} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β}) + c_{1} J_{- \frac{b}{β}} (\frac{2 \sqrt{- a} \sqrt{c} x^{β / 2}}{β}))}}}$ ✓ Maple : cpu = 0.102 (sec), leaf count = 171

dsolve(x*diff(y(x),x)+a*y(x)^2-b*y(x)-c*x^beta = 0,y(x))

$y (x) = \frac{- (BesselY (\frac{b + β}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β}) c_{1} + BesselJ (\frac{b + β}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β})) \sqrt{- a c} x^{\frac{β}{2}} + b (BesselY (\frac{b}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β}) c_{1} + BesselJ (\frac{b}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β}))}{a (BesselY (\frac{b}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β}) c_{1} + BesselJ (\frac{b}{β}, \frac{2 \sqrt{- a c} x^{\frac{β}{2}}}{β}))}$

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