a. Explanation Given: d y d t = t 2 y 3 + y 3 ; y ( 0 ) = 1 Formula used: Linear deferential equation: A general linear differential equation of order n, in the dependent variable y and the independent variable x, is an equation that can be expressed in the form − a 0 ( x ) d n y d x n + a 1 ( x ) d n − 1 y d x n − 1 + .... + a n − 1 ( x ) d y d x + a n ( x ) y = b ( x ) where a 0 is not identically 0. Homogeneous equation: In a leaner first order differential equation, d y d x = f ( x , y ) if f ( α x , α y ) = α n f ( x , y ) then it is inhomogeneous in nature, of degree = n . Calculation: As from the above, d y d t = t 2 y 3 + y 3 ; ⇒ d y d t − ( t 2 + 1 ) y 3 = 0 The derivative given above is not similar to the general equation, and therefore, it should be a non-linear differential equation b. To determine solution for the given differential equation.

4th Edition

ISBN: 9780495561989

Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall

Publisher: Cengage Learning

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Chapter 1, Problem 33RE

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To specify: Whether the given differential equation is autonomous, linear, homogeneous type or not.

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solution for the given differential equation.

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Differential Equations

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To specify: Whether the given differential equation is autonomous, linear, homogeneous type or not.

Solution Summary: The author specifies whether the given differential equation is an autonomous, linear, homogeneous type and it is separable.

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