Explanation Given: The initial value problem: d y d t = y 2 + 5 y , y ( 0 ) = − 2 . Formula used: The integration rules: ∫ d x x = ln x + C Calculation: Solve the given differential equation by separating the variables as follows: d y d t = y 2 + 5 y y y 2 + 5 d y = d t ∫ y y 2 + 5 d y = ∫ d t ∫ 1 2 ( 2 y y 2 + 5 ) d y = ∫ d t 1 2 ln ( y 2 + 5 ) = t + c ....... ( 1 ) Now, use the initial condition y ( 0 ) = − 2 in equation (1)

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ISBN: 9781133109044

Author: Blanchard, Devaney, and Hall

Publisher: ACME

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Chapter 1.2, Problem 38E

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To solve the initial value problem dydt=y2+5y, y(0)=−2 .

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Chapter 1.2, Problem 37E

Chapter 1.2, Problem 39E

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To solve the initial value problem d y d t = y 2 + 5 y , y ( 0 ) = − 2 .

Solution Summary: The author explains how to solve the differential equation by separating the variables.

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To solve the initial value problem dydt=y2+5y, y(0)=−2 .

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