Check sibling questions

Example 2 - Verify that y = e-3x is a solution of y'' + y' - 6y = 0

Example 2 - Chapter 9 Class 12 Differential Equations - Part 2
Example 2 - Chapter 9 Class 12 Differential Equations - Part 3


Transcript

Example 2 Verify that the function 𝑦=𝑒^(βˆ’3π‘₯) is a solution of the differential equation (𝑑^2 𝑦)/(𝑑π‘₯^2 )+𝑑𝑦/𝑑π‘₯βˆ’6𝑦=0 𝑦=𝑒^(βˆ’3π‘₯) π’…π’š/𝒅𝒙=𝑑(𝑒^(βˆ’3π‘₯) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯=γ€–βˆ’3 𝑒〗^(βˆ’3π‘₯) (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 )=𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯) =𝑑(γ€–βˆ’3 𝑒〗^(βˆ’3π‘₯) )/𝑑π‘₯ =βˆ’3 𝑑(𝑒^(βˆ’3π‘₯) )/𝑑π‘₯ =βˆ’3 Γ— (γ€–βˆ’3 𝑒〗^(βˆ’3π‘₯) ) = γ€–9 𝑒〗^(βˆ’3π‘₯) Now, we have to verify (𝑑^2 𝑦)/(𝑑π‘₯^2 )+𝑑𝑦/𝑑π‘₯βˆ’6𝑦=0 Solving L.H.S (𝑑^2 𝑦)/(𝑑π‘₯^2 )+𝑑𝑦/𝑑π‘₯βˆ’6𝑦 Putting values = γ€–9 𝑒〗^(βˆ’3π‘₯)+(βˆ’3𝑒^(βˆ’3π‘₯) )βˆ’6(𝑒^(βˆ’3π‘₯) ) =γ€–9 𝑒〗^(βˆ’3π‘₯)βˆ’3𝑒^(βˆ’3π‘₯)βˆ’6𝑒^(βˆ’3π‘₯) =γ€–9 𝑒〗^(βˆ’3π‘₯)βˆ’9𝑒^(βˆ’3π‘₯) =0 = R.H.S ∴ Hence Verified

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.