Example 2 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Gen and Particular Solution
Ex 9.2, 12 (MCQ) Important
Question 11 (MCQ) Deleted for CBSE Board 2024 Exams
Question 12 (MCQ) Important Deleted for CBSE Board 2024 Exams
Example 2 You are here
Ex 9.2, 1
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Example 3 Important
Ex 9.2, 7
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Ex 9.2, 4 Important
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Ex 9.2, 6 Important
Example 19
Misc 2 (i)
Gen and Particular Solution
Last updated at April 16, 2024 by Teachoo
Example 2 Verify that the function 𝑦=𝑒^(−3𝑥) is a solution of the differential equation (𝑑^2 𝑦)/(𝑑𝑥^2 )+𝑑𝑦/𝑑𝑥−6𝑦=0 𝑦=𝑒^(−3𝑥) 𝒅𝒚/𝒅𝒙=𝑑(𝑒^(−3𝑥) )/𝑑𝑥 𝑑𝑦/𝑑𝑥=〖−3 𝑒〗^(−3𝑥) (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )=𝑑/𝑑𝑥 (𝑑𝑦/𝑑𝑥) =𝑑(〖−3 𝑒〗^(−3𝑥) )/𝑑𝑥 =−3 𝑑(𝑒^(−3𝑥) )/𝑑𝑥 =−3 × (〖−3 𝑒〗^(−3𝑥) ) = 〖9 𝑒〗^(−3𝑥) Now, we have to verify (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )+𝒅𝒚/𝒅𝒙−𝟔𝒚=𝟎 Solving L.H.S (𝑑^2 𝑦)/(𝑑𝑥^2 )+𝑑𝑦/𝑑𝑥−6𝑦 Putting values = 〖9 𝑒〗^(−3𝑥)+(−3𝑒^(−3𝑥) )−6(𝑒^(−3𝑥) ) =〖9 𝑒〗^(−3𝑥)−3𝑒^(−3𝑥)−6𝑒^(−3𝑥) =〖9 𝑒〗^(−3𝑥)−9𝑒^(−3𝑥) =𝟎 = R.H.S ∴ Hence Verified