Example 2 - Chapter 9 Class 12 Differential Equations
Last updated at May 29, 2018 by Teachoo
Transcript
Example 2 Verify that the function 𝑦= 𝑒−3𝑥 is a solution of the differential equation 𝑑2𝑦𝑑 𝑥2+ 𝑑𝑦𝑑𝑥−6𝑦=0 𝑦= 𝑒−3𝑥 𝒅𝒚𝒅𝒙= 𝑑 𝑒−3𝑥𝑑𝑥 𝑑𝑦𝑑𝑥= −3 𝑒−3𝑥 𝒅𝟐𝒚𝒅 𝒙𝟐= 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑𝑑𝑥 −3 𝑒−3𝑥 =−3 𝑑 𝑒−3𝑥𝑑𝑥 =−3 × −3 𝑒−3𝑥 = 9 𝑒−3𝑥 Now, we have to verify 𝑑2𝑦𝑑 𝑥2+ 𝑑𝑦𝑑𝑥−6𝑦=0 Solving L.H.S 𝑑2𝑦𝑑 𝑥2+ 𝑑𝑦𝑑𝑥−6𝑦 Putting values = 9 𝑒−3𝑥+ −3 𝑒−3𝑥−6 𝑒−3𝑥 = 9 𝑒−3𝑥−−3 𝑒−3𝑥−6 𝑒−3𝑥 = 9 𝑒−3𝑥−−9 𝑒−3𝑥 =0 = R.H.S ∴ Hence Verified
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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.