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(ax2+bx+c)2(ddxy(x)+(y(x))2)+A=0
Mathematica: cpu = 1.467686 (sec), leaf count = 704 {{y(x)→−−2aax2+bx+cexp(−4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac)(b2−4ac)((2ax+b)24ac−b2+1)+(2ax+b)exp(−4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac)2b2−4ac1−4Ab2−4acax2+bx+c+c1(2a1−4Ab2−4acx(ax+b)+cexp(4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac)b2−4ac((2ax+b)24ac−b2+1)+(2ax+b)exp(4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac)2x(ax+b)+c)c1x(ax+b)+c(−exp(4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac))−ax2+bx+cexp(−4ac−b21−4Ab2−4actan−1(2ax+b4ac−b2)b2−4ac)b2−4ac1−4Ab2−4ac}}
Maple: cpu = 0.234 (sec), leaf count = 846 {y(x)=−2a−4ac+b2(2ax+b+i4ac−b2)(i4ac−b2−2ax−b)(−i4ac−b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)−1/2a−4ac+b2−4ac−b2+4Aa2−4ac−b2+4Aa2_C1a+i4ac−b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)1/2a−4ac+b2−4ac−b2+4Aa2−4ac−b2+4Aa2a+2−4ac+b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)−1/2a−4ac+b2−4ac−b2+4Aa2_C1ax+2−4ac+b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)1/2a−4ac+b2−4ac−b2+4Aa2ax+−4ac+b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)−1/2a−4ac+b2−4ac−b2+4Aa2_C1b+−4ac+b2(i4ac−b2−2ax−b2ax+b+i4ac−b2)1/2a−4ac+b2−4ac−b2+4Aa2b)(_C1(i4ac−b2−2ax−b2ax+b+i4ac−b2)−1/2a−4ac+b2−4ac−b2+4Aa2+(i4ac−b2−2ax−b2ax+b+i4ac−b2)1/2a−4ac+b2−4ac−b2+4Aa2)−1}
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