Explanation Given: y ' + ( tan x ) y = cos 2 x and y ( π ) = 2 Formula used: ∫ x n d x = 1 n + 1 x n + 1 ……………. (1) ∫ cos x d x = sin x + c …………….(2) ∫ tan x d x = ln sec x + c …………… (3) cos x = 1 sec x ……………….(4) Calculation: Consider the given equation y ' + ( tan x ) y = cos 2 x According to the rule of linear differential equations, every linear differential equation can be represented in the form of: d y d x + P . y = Q where P and Q are functions of x and integrating factor I . F = e ∫ P d x And solution is e ∫ P d x . y = ∫ Q . e ∫ P d x d x Converting the given equation into standard form d y d x + ( tan x ) y = cos 2 x P = tan x and Q = cos 2 x I ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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The general solution of y ' + ( tan x ) y = cos 2 x

Solution Summary: The author explains the rule of linear differential equations, where P and Q are functions of x and integrating factor I.

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The general solution of $y' + (\tan x) y = \cos^{2} x$

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The general solution of y ' + ( tan x ) y = cos 2 x

Solution Summary: The author explains the rule of linear differential equations, where P and Q are functions of x and integrating factor I.

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The general solution of y'+(tanx)y=cos2x

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Chapter 10 Solutions

The general solution of $y' + (\tan x) y = \cos^{2} x$