Verify that the indicated function y = ϕ(x) is an explicit solution of the given first-order differential equation. (y − x)y' =
1 answer:
Answer:
The function is not a solution of the given differential equation.
Step-by-step explanation:
Verify that a function f (x) is a solution to a differential equation, consists in finding the derivatives of the function and entering them into the equation. If the given function, indeed, is the solution, equality must be checked.
The function is not a solution of the given differential equation
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Answer:
see explanation
Step-by-step explanation:
Given
9n² - n - = 0 ← multiply through by 3 to clear the fraction
27n² - 3n - 2 = 0 ← factoring
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 27 × - 2 = - 54 and sum = - 3
The factors are - 9 and + 6
Use these factors to split the n- term
27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )
9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term
(3n - 1)(9n + 2) = 0
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n =
9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = -