Explanation Formula used: ∫ x n d x = 1 n + 1 x n + 1 …………….( 1) ∫ ( u ( x ) . v ( x ) ) d x = u ( x ) ∫ v ( x ) d x − ∫ u ' ( x ) ∫ v ( x ) d x …………….(2) ∫ e x d x = e x + c ……………( 3) Calculation: Consider the given equation y ' + n y = cos x ⇒ d y d x + n y = cos x According to linear differential equation, 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 of above equation is given by I . F = e ∫ P d x And solution is y · e ∫ P d x = ∫ Q . e ∫ P d x d x Converting the given equation into standard form, we get d y d x + n y = cos x where, P = n and Q = cos x I . F = e ∫ n d x ⇒ I

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.5, Problem 32E

To determine

The general solution of the differential equation y'+ny=cosx .

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Chapter 10.5, Problem 31E

Chapter 10.5, Problem 33E

Chapter 10 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The general solution of the differential equation y ' + n y = cos x .

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The general solution of the differential equation y'+ny=cosx .

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Chapter 10 Solutions