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y′(x)−(a0+a1x+a2x2+a3x3a0+a1y(x)+a2y(x)2+a3y(x)3)2/3=0 ✓ Mathematica : cpu = 0.99918 (sec), leaf count = 733
Solve[3(a0+y(x)(a1+y(x)(a2+a3y(x))))2/3(y(x)−Root[#13a3+#12a2+#1a1+a0&,1])F1(53;−23,−23;83;Root[a3#13+a2#12+a1#1+a0&,1]−y(x)Root[a3#13+a2#12+a1#1+a0&,1]−Root[a3#13+a2#12+a1#1+a0&,2],Root[a3#13+a2#12+a1#1+a0&,1]−y(x)Root[a3#13+a2#12+a1#1+a0&,1]−Root[a3#13+a2#12+a1#1+a0&,3])5(y(x)−Root[#13a3+#12a2+#1a1+a0&,2]Root[#13a3+#12a2+#1a1+a0&,1]−Root[#13a3+#12a2+#1a1+a0&,2])2/3(y(x)−Root[#13a3+#12a2+#1a1+a0&,3]Root[#13a3+#12a2+#1a1+a0&,1]−Root[#13a3+#12a2+#1a1+a0&,3])2/3=3(a0+x(a1+x(a2+a3x)))2/3(x−Root[#13a3+#12a2+#1a1+a0&,1])F1(53;−23,−23;83;Root[a3#13+a2#12+a1#1+a0&,1]−xRoot[a3#13+a2#12+a1#1+a0&,1]−Root[a3#13+a2#12+a1#1+a0&,2],Root[a3#13+a2#12+a1#1+a0&,1]−xRoot[a3#13+a2#12+a1#1+a0&,1]−Root[a3#13+a2#12+a1#1+a0&,3])5(x−Root[#13a3+#12a2+#1a1+a0&,2]Root[#13a3+#12a2+#1a1+a0&,1]−Root[#13a3+#12a2+#1a1+a0&,2])2/3(x−Root[#13a3+#12a2+#1a1+a0&,3]Root[#13a3+#12a2+#1a1+a0&,1]−Root[#13a3+#12a2+#1a1+a0&,3])2/3+c1,y(x)]
✓ Maple : cpu = 0.363 (sec), leaf count = 91
{∫y(x)(_a3a3+_a2a2+_aa1+a0)23d_a+∫x−(_a3a3+_a2a2+_aa1+a0a3(y(x))3+a2(y(x))2+a1y(x)+a0)23(a3(y(x))3+a2(y(x))2+a1y(x)+a0)23d_a+_C1=0}
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