Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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D Y D X + Y Tan X = X N Cos X , N ≠ − 1 - Mathematics

Sum

`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`

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Solution

We have,

`(dy)/(dx)+ y tan x = x^n cos x`

\[\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}\]

\[P = \tan x \]

\[Q = x^n \cos x\]

Now,

\[I . F . = e^{\int\tan x dx} \]

\[ = e^{\log\left( sec x \right)} \]

\[ = \sec x\]

So, the solution is given by

\[y \times I . F . = \int Q \times I . F . dx + C\]

\[ \Rightarrow y \sec x = \int x^n \cos x \sec x\ dx + C\]

\[ \Rightarrow y \sec x = \int x^n dx + C\]

\[ \Rightarrow y \sec x = \frac{x^{n + 1}}{n + 1} + C\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 61 | Page 146
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