Let f and g be function satisfying f(0)=1, g(0)=0 and then f

JEE MainMathematicsEasyDifferentiation

Let f and g be function satisfying f(0)=1, g(0)=0 and
$f^{'}(x) = g(x),g^{'}(x) = f(x)$ then f

Show answer and solution

f^{''}(x) = f(x)

\Rightarrow f(x) = Ae^{x} + Be^{- x}

A + B = 1

f^{'}(x) = Ae^{x} - Be^{- x}

f^{'}(0) = g(0) = 0 \Rightarrow A = B

f(x) = \frac{1}{2}(e^{x} + e^{- x})

Source: Grass-G / M-12 Mathematics Paper 2 Nov.docx

Scan any doubt from your notes and get a whiteboard explanation.