# Example 19 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 19 Find the general solution of the differential equation 𝑑𝑦𝑑𝑥−𝑦= cos𝑥 Differential equation is of the form 𝑑𝑦𝑑𝑥+𝑃𝑦=𝑄 where P = −1 & Q = cos x IF = e 𝑝𝑑𝑥 IF = e− 1𝑑𝑥 IF = 𝑒−𝑥 Solution is y(IF) = 𝑄×𝐼𝐹 𝑑𝑥+𝑐 𝑦 𝑒−𝑥 = 𝑒−𝑥 cos𝑥+𝑐 Let I = 𝑒−𝑥 cos𝑥 𝑑𝑥 I = cos x 𝑒−𝑥𝑑𝑥− − sin𝑥 𝑒−𝑥𝑑𝑥𝑑𝑥 I = −𝑒−𝑥cos x − − sin𝑥 (− 𝑒−𝑥)𝑑𝑥 I = −e−x cos x − 𝑒−𝑥 sin𝑥 𝑑𝑥 I = −e−x cos x − sin𝑥 𝑒−𝑥𝑑𝑥− (cos𝑥 𝑒−𝑥𝑑𝑥) dx I = −e−x cos x − − 𝑒−𝑥 sin𝑥 − − 𝑒−𝑥 cos𝑥𝑑𝑥 I = −e−x cos x − − 𝑒−𝑥 sin𝑥+ 𝑒−𝑥 cos𝑥𝑑𝑥 I = −e−x cos x + 𝑒−𝑥 sin𝑥− 𝒆−𝒙 𝒄𝒐𝒔𝒙𝒅𝒙 I = e−x (sin x − cos x) − I 2I = e−x (sin x − cos x) I = 𝑒−𝑥2 (sin x − cos x) From (1) y 𝑒−𝑥 = 𝑒−𝑥 cos𝑥+𝑐 y 𝑒−𝑥 = 𝑒−𝑥2 (sin x − cos x) + c y = 𝟏𝟐 (sin x − cos x) + c 𝒆−𝒙

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Chapter 9 Class 12 Differential Equations

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.