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{x″(t)=ax(t)+by(t),y″(t)=cx(t)+dy(t)} ✓ Mathematica : cpu = 0.546093 (sec), leaf count = 5647
{{x(t)→e−(a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c1+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c1+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c1+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c1−2a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c2−2a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c2+2a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c2+2a2−2da+d2+4bca+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c2+d(a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2(a+d−a2−2da+d2+4bcc1−2c2)+a+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(a+d−a2−2da+d2+4bcc1+2c2)+a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2(2c2−a+d+a2−2da+d2+4bcc1)−a+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2(a+d+a2−2da+d2+4bcc1+2c2))+a(a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2(a+d+a2−2da+d2+4bcc1−2c2)+a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2(2c2−a+d−a2−2da+d2+4bcc1)−a+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(a+d−a2−2da+d2+4bcc1+2c2)+a+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2(a+d+a2−2da+d2+4bcc1+2c2))+2ba+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c3−2ba+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c3−2ba+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c3+2ba+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c3−22ba+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c4+22ba+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c4−22ba+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c4+22ba+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c4)4a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc,y(t)→e−(a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(2c(a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2(a+d+a2−2da+d2+4bcc1−2c2)+a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2(2c2−a+d−a2−2da+d2+4bcc1)−a+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(a+d−a2−2da+d2+4bcc1+2c2)+a+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2(a+d+a2−2da+d2+4bcc1+2c2))+da+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c3+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c3−da+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c3+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c3−da+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c3+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c3+da+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c3+a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c3−2da+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c4−2a2−2da+d2+4bca+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2c4+2da+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c4−2a2−2da+d2+4bca+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2c4−2da+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c4+2a2−2da+d2+4bca+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2c4+2da+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c4+2a2−2da+d2+4bca+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2c4+a(a+d+a2−2da+d2+4bcea+d+a2−2da+d2+4bct2(a+d−a2−2da+d2+4bcc3−2c4)+a+d+a2−2da+d2+4bce(2a+d−a2−2da+d2+4bc+a+d+a2−2da+d2+4bc)t2(a+d−a2−2da+d2+4bcc3+2c4)+a+d−a2−2da+d2+4bcea+d−a2−2da+d2+4bct2(2c4−a+d+a2−2da+d2+4bcc3)−a+d−a2−2da+d2+4bce(a+d−a2−2da+d2+4bc+2a+d+a2−2da+d2+4bc)t2(a+d+a2−2da+d2+4bcc3+2c4)))4a2−2da+d2+4bca+d−a2−2da+d2+4bca+d+a2−2da+d2+4bc}}
✓ Maple : cpu = 0.14 (sec), leaf count = 360
{{x(t)=_C1e−t2−2a2−2da+4bc+d2+2a+2d+_C2et2−2a2−2da+4bc+d2+2a+2d+_C3e−t22a2−2da+4bc+d2+2a+2d+_C4et22a2−2da+4bc+d2+2a+2d,y(t)=12b(−_C1(a2−2da+4bc+d2+a−d)e−t2−2a2−2da+4bc+d2+2a+2d−_C2(a2−2da+4bc+d2+a−d)et2−2a2−2da+4bc+d2+2a+2d−(_C3e−t22a2−2da+4bc+d2+2a+2d+_C4et22a2−2da+4bc+d2+2a+2d)(−a2−2da+4bc+d2+a−d))}}
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