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D Y D X − Y Tan X = E X Sec X - Mathematics

Sum

\[\frac{dy}{dx} - y \tan x = e^x \sec x\]

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Solution

We have,

\[\frac{dy}{dx} - y \tan x = e^x \sec x\]

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

\[P = - \tan x \]

\[Q = e^x \sec x\]

Now,

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

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

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

\[ = \cos x\]

So, the solution is given by

\[y \cos\ x = \int\left( \cos x\ e^x \sec x \right) dx + C\]

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

\[ \therefore y \cos\ x = e^x + C\]

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APPEARS IN

RD Sharma Class 12 Maths
Chapter 22 Differential Equations
Revision Exercise | Q 42 | Page 146
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