Show that y = sin(tan1 x + C) is the general solution of y' = 1

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Show that y = sin(tan−1 x + C) is the general solution of y' = √1 − y²/(1 + x²). Then use the addition formula for the sine function to show that the general solution may be written

y = (cos C)x+ sin C 1 + x

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 12, 2023 11:41 PM

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Show that y = sin(tan1 x + C) is the general solution of y' = 1

Question:

y = (cos C)x+ sin C √1 + x²

Step by Step Answer:

Thus Rewrite dy dx This yields Upon integrating both sides of this equation we f...View the full answer

Calculus

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