MathematicsMedium38×since 2002Q3554Let the solution curve y=y(x)y=y(x)y=y(x) of the differential equation dy dx−3x5tan−1(x3)(1+x6)3/2y=2xexp{x3−tan−1x3(1+x6)} pass through the origin. Then y(1) is equal to : \frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan ^{-1}\left(x^{3}\right)}{\left(1+x^{6}\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^{3}-\tan ^{-1} x^{3}}{\sqrt{\left(1+x^{6}\right)}}\right\} \text { pass through the origin. Then } y(1) \text { is equal to : } dxdy−(1+x6)3/23x5tan−1(x3)y=2xexp{(1+x6)x3−tan−1x3} pass through the origin. Then y(1) is equal to : Aexp(1−π42)\exp \left(\frac{1-\pi}{4 \sqrt{2}}\right)exp(421−π)Bexp(4−π42)\exp \left(\frac{4-\pi}{4 \sqrt{2}}\right)exp(424−π)Cexp(4+π42)\exp \left(\frac{4+\pi}{4 \sqrt{2}}\right)exp(424+π)Dexp(π−442)\exp \left(\frac{\pi-4}{4 \sqrt{2}}\right)exp(42π−4)Check answerSkip