1.

Solve y = p tan p + log (cos p), where, =

Answer»

Given

y=p\TAN p+\log (\COS p)

Differentiating the above w.r.t. x

\FRAC{dy}{dx}=p\sec^p\frac{dp}{dx}+\tan p\frac{dp}{dx}+\frac{1}{\cos p}\times(-\SIN p)\frac{dp}{dx}

\implies p=p\sec^p\frac{dp}{dx}+\tan p\frac{dp}{dx}-\tan p\frac{dp}{dx}

\implies p=p\sec^2p\frac{dp}{dx}

\implies \sec^2p dp=dx

\implies\int \sec^2p dp=\int dx

\implies \tan p=x+c where c is a constant

\implies x=\tan p-c

Thus,

y=p\tan p+\log (\cos p) and x=\tan p-c is parametric solution of the equation, where p is a parameter...................


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