The equation of the curve passing through origin and satisfying the differential equation \( \fr...

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The equation of the curve passing through origin and satisfying the differential equation \( \frac{d y}{d x}=\sin (10 x+6 y) \) is
(a) \( y=\frac{1}{3} \tan ^{-1}\left(\frac{5 \tan 4 x}{4-3 \tan 4 x}\right)-\frac{5 x}{3} \)
(b) \( y=\frac{1}{3} \tan ^{-1}\left(\frac{5 \tan 4 x}{4+3 \tan 4 x}\right)-\frac{5 x}{3} \)
(c) \( y=\frac{1}{3} \tan ^{-1}\left(\frac{3+\tan 4 x}{4-3 \tan 4 x}\right)-\frac{5 x}{3} \)
(d) \( y=\frac{1}{3} \tan \left(\frac{4+\tan 4 x}{3+4 \tan 3 x}\right)+\frac{5 x}{3} \)
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