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The function y(x)=xᵖ is a solution of the differential equation x²y′' −3xy′ −5y=0 for which of the following values of p?

a. 3,
b. 5,
c. 1,
d. 2,
e. 4.

User MeyC
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1 Answer

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Final answer:

The function y(x)=xᵖ is a solution of the differential equation x²y′' −3xy′ −5y=0 for the values of p=3 and p=2.

Step-by-step explanation:

The given differential equation is x²y′' −3xy′ −5y=0. We need to find the values of p for which the function y(x)=xᵖ is a solution to this equation.

To solve this, we substitute y(x)=xᵖ into the differential equation and simplify. We differentiate y(x) twice and substitute the results into the equation.

By solving the resulting equation, we find that the value of p must be 3 or 2 to satisfy the differential equation. Therefore, the correct options are a. 3 and d. 2.

User Farrukh Tulkunov
by
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