Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 9 of Exercise 9.5

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In each of the question, show that the given differential equation is homogeneous and solve each of them.







Here, putting x = kx and y = ky




= k0.f(x,y)


Therefore, the given differential equation is homogeneous.







To solve it we make the substitution.


y = vx


Differentiating eq. with respect to x, we get












Integrating both sides, we get




Put, logv – 1 = t




logt


log(logv - 1)


log(logv - 1) – log(v) = log(x) + log(c) (From (i) eq.)







The required solution of the differential equation.


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