Probability and complex function: Unit V: Ordinary Differential Equations

(d) problems based on R.H.S = eax + sin ax(or) eax + cos ax

Solved Example Problems | Ordinary Differential Equations

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Probability and complex function: Unit V: Differential equations : I. (d) problems based on R.H.S = eax + sin ax(or) eax + cos ax : Examples

I. (d) PROBLEMS BASED ON R.H.S = e^ax + sin ax(or) e^ax + cos ax

Example 5.1.27 Solve (D² + 2D + 2) y = e^-2x + cos 2x

[A.U N/D 2016 R-13]

Solution: Given: (D² + 2D + 2) y = e^-2x + cos 2x

The auxiliary equation is m² + 2m + 2 = 0

⇒ m = - 1 ± i

C.F = e^-x [4 cos x + B sin x]

Example 5.1.28 Solve: (D² - 3D + 2) y = 2 cos (2x + 3 ) + 2e^x

[A.U Jan. 2005, N/D 2009, N/D 2011]

Solution: Given:

Example 5.1.29. Solve: (D³ - 2D² + 4D - 8) y = e^2x + sin x cos x

Solution :

The auxiliary equation is m³ - 2m² + 4m − 8 = 0

Probability and complex function: Unit V: Ordinary Differential Equations : Tag: : Solved Example Problems | Ordinary Differential Equations - (d) problems based on R.H.S = eax + sin ax(or) eax + cos ax

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