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CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

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Question : 3 of 36
Marks: +1, -0
If y=Ae5x+Be−5xy = A e^{5x} + B e^{-5x}, then   d2ydx2\;\frac{d^2 y}{dx^2} is equal to
Solution:     👈: Video Solution
Given:
y=Ae5x+Be−5xy = A e^{5x} + B e^{-5x}
∴  dydx=5Ae5x−5Be−5x\therefore\;\frac{dy}{dx}=5A e^{5x}-5B e^{-5x}
⇒  d2ydx2=25Ae5x+25Be−5x\Rightarrow\;\frac{d^2 y}{dx^2}=25A e^{5x}+25B e^{-5x}
⇒  d2ydx2=25y.\Rightarrow\;\frac{d^2 y}{dx^2}=25 y.
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