Solve the differential equation ` (dy)/(dx) + y tan x = 2x + x ^(2)tan

1.	Solve the differential equation ` (dy)/(dx) + y tan x = 2x + x ^(2)tanx `
Answer» The given differential equation is of the form `(dy)/(dx) + Py = Q`, where` P = tan x and Q = 2 x + x ^(2) tanx.` Thus, the givebn differential equation is linear. `IF = e ^( int Pdx) = e ^(int tan x dx ) = e ^( log secx ) = secx` So, its solution is given by `y xx IF = int (Q xx IF )dx +C`, i.e, `y xx secx = int (2x + x ^(2) tanx ) sec x dx + C ` ` " "= int 2 x secx dx + int underset ("I") x^(2) underset("II") ( secx tanx ) dx +C ` ` " " = int 2x secx dx + {x ^(2) secx - int 2 x secx dx} + C ` ` " " = x ^(2) sec x + C ` ` therefore y = x ^(2) +C cos x is the required solution.

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