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  ODE No. 900

y′(x)=2a(4ax−y(x)2−1)128a4x3−96a3x2y(x)2+24a2xy(x)4−2ay(x)6+4axy(x)−y(x)3−y(x) ✓ Mathematica : cpu = 0.185562 (sec), leaf count = 381 

DSolve[Derivative[1][y][x] == (2*a*(-1 + 4*a*x - y[x]^2))/(128*a^4*x^3 - y[x] + 4*a*x*y[x] - 96*a^3*x^2*y[x]^2 - y[x]^3 + 24*a^2*x*y[x]^4 - 2*a*y[x]^6),y[x],x]

{{y(x)→Root[8#15a−16#14a2c1−64#13a2x+#12(−2+128a3c1x)+128#1a3x2−256a4c1x2+8ax−1&,1]},{y(x)→Root[8#15a−16#14a2c1−64#13a2x+#12(−2+128a3c1x)+128#1a3x2−256a4c1x2+8ax−1&,2]},{y(x)→Root[8#15a−16#14a2c1−64#13a2x+#12(−2+128a3c1x)+128#1a3x2−256a4c1x2+8ax−1&,3]},{y(x)→Root[8#15a−16#14a2c1−64#13a2x+#12(−2+128a3c1x)+128#1a3x2−256a4c1x2+8ax−1&,4]},{y(x)→Root[8#15a−16#14a2c1−64#13a2x+#12(−2+128a3c1x)+128#1a3x2−256a4c1x2+8ax−1&,5]}} ✓ Maple : cpu = 0.064 (sec), leaf count = 48 

dsolve(diff(y(x),x) = 2*a*(-y(x)^2+4*a*x-1)/(-y(x)^3+4*a*x*y(x)-y(x)-2*a*y(x)^6+24*y(x)^4*a^2*x-96*y(x)^2*a^3*x^2+128*a^4*x^3),y(x))

y(x)2a−116a2(y(x)2−4ax)2+132a3x−8a2y(x)2−c1=0

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