# In each of the following examples, verify that the given function is a solution of the corresponding differential equation. Solution D.E. y = xn x2d2ydx2-n×xdydx+ny=0 - Mathematics and Statistics

Sum

In the following example, verify that the given function is a solution of the corresponding differential equation.

 Solution D.E. y = xn x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0

#### Solution

y = x n

Differentiating w.r.t. x, we get

dy/dx = nx^(n-1)

Again, differentiating w.r.t. x, we get

(d^2y)/dx^2 = n(n-1) x^(n-2)

∴  x^2(d^2y)/dx^2 - nxdy/dx +ny

= n(n-1)x2xn-2 - nx.nxn-1+ nxn

= n(n-1)xn - n2 xn + nxn

=[n(n-1)-n2+n]xn

= 0

∴ x^2 (d^2y)/dx^2 - nxdy/dx + ny = 0

∴ Given function is a solution of the given differential equation.

Concept: Differential Equations
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.1 | Q 2.2 | Page 162