Explanation Given: Differential equation is d y d x + 3 x 2 y − 2 x e − x 3 = 0 , y ( 0 ) = 1000 Approach: General form of linear differential equation of first order is d y d x + P ( x ) y = Q ( x ) Steps to solve linear differential equation of first order are given below: Write given equation in standard form of first order differential equation. Find value of P ( x ) and Q ( x ) . Find integrating factor as I . F = e ∫ P ( x ) d x . Solution of first order linear differential equation is in the form as given below y × ( I . F ) = ∫ ( I . F ) × Q ( x ) d x + C Use initial condition to solve for value of C . Calculation: Given equation is d y d x + 3 x 2 y − 2 x e − x 3 = 0 and condition is y ( 0 ) = 1000 We can rearrange equation as: d y d x + 3 x 2 y − 2 x e − x 3 = 0 d y d x + 3 x 2 y = 2 x e − x 3 On comparing with d y d x + P ( x ) y = Q ( x ) P ( x ) = 3 x 2 , Q ( x ) = 2 x e − x 3 Hence

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 11.2, Problem 22E

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The differential equation dydx+3x2y−2xe−x3=0 which is subjected to initial condition y(0)=1000.

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Chapter 11.2, Problem 21E

Chapter 11.2, Problem 24E

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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The differential equation d y d x + 3 x 2 y − 2 x e − x 3 = 0 which is subjected to initial condition y ( 0 ) = 1000 .

Solution Summary: The author explains how to solve a linear differential equation of first order.

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To find:

The differential equation dydx+3x2y−2xe−x3=0 which is subjected to initial condition y(0)=1000.

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Chapter 11 Solutions

The differential equation d y d x + 3 x 2 y − 2 x e − x 3 = 0 which is subjected to initial condition y ( 0 ) = 1000 .

Solution Summary: The author explains how to solve a linear differential equation of first order.

Concept explainers

Videos

To find: The differential equation dydx+3x2y−2xe−x3=0 which is subjected to initial condition y(0)=1000.

Want to see the full answer?

Chapter 11 Solutions

To find:

The differential equation dydx+3x2y−2xe−x3=0 which is subjected to initial condition y(0)=1000.