Explanation Given: The given differential equation is ( y 2 + 1 ) d x = y sec 2 x d y . Calculation: Consider the given differential equation. ( y 2 + 1 ) d x = y sec 2 x d y (1) Separate the variables in Equation (1). 1 sec 2 x d x = y y 2 + 1 d y cos 2 x d x = y y 2 + 1 d y Use cos 2 x = 1 + cos 2 x 2 in the above equation. ( 1 + cos 2 x 2 ) x d x = y y 2 + 1 d y ( 1 2 + 1 2 cos 2 x ) d x = y y 2 + 1 d y Integrate both the sides of the above equation. ∫ ( 1 2 + 1 2 cos 2 x ) d x = ∫ y y 2 + 1 d y (2) Let y 2 + 1 = u . Then, 2 y d y = d u y d y = 1 2 d u Substitute 1 2 d u for y d y in Equation (2)

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Differential Equations with Boundary-Value Problems (MindTap Course List)

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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