Question

Show that y=a/x+b is a solution of d²y/dx²+2/x dy/dx=0

Answer 1

Answer:

$y=\frac{a}{x}+b\textrm{ satisfies the given equation}\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}+\frac{2}{x}\frac{\mathrm{d} y}{\mathrm{d} x}=0$

Step-by-step explanation;-

We have already been provided that,

$It\ is\ Given-:y=\frac{a}{x}+b$

$we\ have\ to\ show-:\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}+\frac{2}{x}\frac{\mathrm{d} y}{\mathrm{d} x}=0$

$y=\frac{a}{x}+b$

$\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{-a}{x^{2}}$

$\frac{\mathrm{d}^2 y}{\mathrm{d} x^2}=\frac{2a}{x^{3}}$

$\textrm{Now putiting the value in the given equation we get,}$

$\frac{2a}{x^{3}}+\frac{-2}{x}\times\frac{a}{x^{2}}$

$\frac{2a}{x^{3}}+\frac{-2a}{x^{3}}$

$\textrm{=0 Which is equal to R.H.S}$

$\textrm{Hence y =}\frac{a}{x}+b\textrm{Satisfies the given equation}$