The solution of the differential equation dy/dx = tan ≤ft(y/x)+≤ft(y/x) is

Correct Answer is : sin (yx)≤ft(y/x)(xy) = cx

Correct Answer is : sin (yx)≤ft(y/x)(xy) = cx

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MHT CET 2017 Math Solved Paper

Question : 13 of 50

Marks: +1, -0

\frac{dy}{dx}

\left(\frac{y}{x}\right)+\left(\frac{y}{x}\right)

Solution:

(b) We have,

\frac{dy}{dx}=\tan\left(\frac{y}{x}\right)+\left(\frac{y}{x}\right)

..........(i)

Since, it is homogeneous differential equation After putting,

y=Vx,

we get

\frac{dy}{dx}=V+x\frac{dV}{dx}

V+x\frac{dV}{dx}

\tan V+V

[From (i) ]

⇒

x\frac{dV}{dx}=\tan V

⇒

\frac{1}{\tan V}dV=\frac{1}{x}dx

After integrating on both sides, we get

\int\frac{1}{\tan V}\,dV=\int\frac{1}{x}\,dx

⇒ ∫cot VdV = logx + logc

⇒ log sin V = log(xc)

⇒ sin v = xc

Hence, sin

\left(\frac{y}{x}\right)

= xc

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