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प्रश्न
Find the solution of `"dy"/"dx"` = 2y–x.
उत्तर
The given differential equation is
`"dy"/"dx"` = 2y–x
⇒ `"dy"/"dx" = 2^y/2^x`
Separating the variables, we get
`"dy"/2^y = "dx"/2^x`
⇒ `2^-y "d"y = 2^-x "d"x`
Integrating both sides, we get
`int 2^-y "d"y = int 2^-x "d"x`
`(-2^-y)/log2 = (-2^-x)/log2 + "c"`
⇒ `-2^-y = -2^-x + "c" log 2`
⇒ `-2^-y + 2^-x = "c" log 2`
⇒ `2^-x - 2^-y` = k .....[Where c log 2 = k]
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