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प्रश्न
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` |
उत्तर
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.
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