Determine the equation of the curve... - Solved

Question 6

Mathematics Differential Equations Easy

Determine the equation of the curve passing through the origin, in the form of \( y=f(x) \) , which satisfies the differential equation \( \frac{\mathrm{dy}}{\mathrm{dx}}=\sin (10 \mathrm{x}+6 \mathrm{y}) \) .

(A) \( 5 x+3 y=\left[\tan ^{-1}\left(\frac{5 \tan 4 x}{4-3 \tan 4 x}\right)-5 x\right] \)

(B) \( 5 x+3 y=\left[\tan ^{-1}\left(\frac{5 \tan 4 x}{4-3 \tan 4 x}\right)+7 x\right] \)

(C) \( 5 x-3 y=\left[\tan ^{-1}\left(\frac{5 \tan 4 x}{4-3 \tan 4 x}\right)-8 x\right] \)

(D) \( 9 x+7 y=\left[\tan ^{-1}\left(\frac{5 \tan 4 x}{4-3 \tan 4 x}\right)-5 x\right] \)

✓ Correct Answer: Option A Verified Solution

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Correct Option is A. Practice regular variations of this Differential Equations concept to build speed and accuracy.

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Question 6

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