Solve the following: ddydx+ycosx=sinxcosx - Business Mathematics and Statistics

प्रश्न

Solve the following:

`("d"y)/(""dx) + y cos x = sin x cos x`

योग

उत्तर

It is of the form `("d"y)/("d"x) + "P"y` = Q

Here P = cos x

Q = sin x cos x

`int "P""d"x = int cos x "d"x = sinx`

I.F = `"e"^(int pdx) = "e"^(sinx)`

The required solution is

y(I.F) = `int "Q" ("I.F") "d"x + "c"`

y(e^sinx) = `int "Q" ("I" - "F") "d"x + "c"`

y(e^sinx) = `int "te"^"t" "dt" + "c"`

y e^sinx = `int ("t") ("e"^"t") - int ("e"^"t") "dt" + "c"`

y e^sinx = `["te"^"t" - "e"^"t"] + "c"`

y e^sinx = `"e"^"t" ["t" - 1] + "c"`

y e^sinx = `"e"^sinx [sin x - 1] + "c"`

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Solution of First Order and First Degree Differential Equations

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 2 Q 1 Q 3

अध्याय 4: Differential Equations - Exercise 4.4 [पृष्ठ ९४]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board

अध्याय 4 Differential Equations
Exercise 4.4 | Q 2 | पृष्ठ ९४

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