InterviewSolution
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InterviewSolution
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Solve: `dy / dx + y secx = tanx` |
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Answer» The given equation is of the form ` (dy)/(dx) + Py = Q`, where ` P = sec x and Q = tan x ` Thus, the given equation is linear. `IF =e ^( int Pdx) = e ^( int sec x dx ) = e ^(log (sec x + tan x ) ) = (sec x + tanx )` So, the required solution is ` y xx IF = int { Q xx( IF ) }dx + C`, i.e, `y (secx + tan x ) = int tan x (sec x + tan x ) dx + C ` ` " " = int sec x tan x dx = int tan ^(2) x dx + C ` ` " " = sec x + int (sec ^(2) x - 1 ) dx + C ` ` " " =sec x + tanx - x + C`. Hence, ` y (sec x +tan x ) =sec x + tanx - x+ C ` is the required solution. |
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