Explanation Given Information: The differential equation is y ′ = 1 + 4 y 2 . Concept used: Use the following integration to solve the problem. ∫ 1 1 + a 2 x 2 d x = 1 a tan − 1 a x + c Here, c is an arbitrary constant. Calculation: Consider the given equation, y ′ = 1 + 4 y 2 Rewrite the given equation in d y d x form and separate the variables, d y d x = 1 + 4 y 2 d y 1 + 4 y 2 = d x Integrate the above equation where c is an arbitrary constant. ∫ d y 1 + 4 y 2 = ∫ d x ∫ d y 1 + 2 y 2 = ∫ d x

Calculus: Early Transcendentals, Enhanced Etext

12th Edition

ISBN: 9781119777984

Author: Howard Anton; Irl C. Bivens; Stephen Davis

Publisher: Wiley Global Education US

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Chapter 8 Solutions

Calculus: Early Transcendentals, Enhanced Etext

Ch. 8.1 - Match each differential equation with its family...Ch. 8.1 - If y=C1e2x+C2xe2x is the general solution of a...Ch. 8.1 - The graph of a differentiable function y=yx passes...Ch. 8.1 - A glass of ice water with a temperature of 36F is...Ch. 8.1 - Confirm that y=3ex3 is a solution of the...Ch. 8.1 - Confirm that y=14x4+2cosx+1 is a solution of the...Ch. 8.1 - State the order of the differential equation, and...Ch. 8.1 - Prob. 4ES Ch. 8.1 - Determine whether the statement is true or false....Ch. 8.1 - Determine whether the statement is true or false....

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The solution of differential equation y ′ = 1 + 4 y 2 with the help of separation of variables method.

Solution Summary: The author explains how to solve the differential equation yprime with the help of separation of variables method.

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