Explanation The differential equation is t y ′ ( t ) = 1 , y ( 1 ) = 2 , t > 0 . Consider the equation t y ′ ( t ) = 1 . This implies, y ′ ( t ) = 1 t . d y d t = 1 t d y = d t t Therefore, the given equation is separable. Integrate both sides of the equation. ∫ d y = ∫ d t t y ( t ) = ln | t | + c y ( t ) = ln t + c (1) Use the given initial condition y ( 1 ) = 2 to evaluate the constant c

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Differential Equations

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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Chapter D1.3, Problem 17E

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Whether the given equation is separable or not and find the solution if it separable.

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Chapter D1.3, Problem 16E

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Chapter D1 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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Whether the given equation is separable or not and find the solution if it separable.

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