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dangina [55]
3 years ago
9

Is the given function phi(x) = x^2 - x^-1 an explicit solution to the linear equation d^2y/dx^2 - 2/x^2 y = 0? Circle your answe

r. (a) yes (b) no
Mathematics
1 answer:
mart [117]3 years ago
3 0

Answer:

Yes

Step-by-step explanation:

We are given that a function \phi(x)=x^2-x^{-1}

We have to find that given function is an explicit solution to the linear equation

\frac{d^2y}{dx^2}-\frac{2}{x^2}y=0

If given function is an explicit solution of given linear equation then it satisfied the given differential equation

Differentiate w.r.t x

Then we get \phi'(x)=2x+x^{-2}

Again differentiate w.r.t x

Then we get

\phi''(x)=2-\frac{2}{x^3}

Substitute all values in the given differential equation

2-\frac{2}{x^3}-\frac{2}{x^2}(x^2-x^{-1})

=2-\frac{2}{x^3}-2+\frac{2}{x^3}=0

Hence, given function is an explicit solution of given differential equation.

Therefore, answer is yes.

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