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Question
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
Solution
Given differential equation is `(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/(e^x + 1/e^x)`
⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/((e^(2x) + 1)) xx e^x`
⇒ `(dy)/(dx)` = 3e3x
⇒ dy = 3e3xdx
Integrating both sides, we get
`intdy = 3inte^(3x)dx`
⇒ y = `3 e^(3x)/3 + C`
y = `e^(3x) + C`
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