Show that every member of the family of functions y = (6 ln(x) + C)/x , x > 0, is a solution of the differential equation x2y
' + xy = 6. (Simplify as much as possible.) y = 6 ln(x) + C x ⇒ y' = 6x · (1/x) − (6 ln(x) +C) x2 LHS = x2y' + xy = x2 · x2 + x · 6 ln(x) + C x = + 6 ln(x) + C = = RHS, so y is a solution of the differential equation.
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Answer:
a = -1, b = -2.5
Step-by-step explanation:
Rule for the dilation of a vector by a scale factor of k is,
(x, y) → (kx, ky)
BY using this rule for a vector by a scale factor of 2.5
→
Followed by the rotation by 90° Or radians,
Rule for rotation of a vector by 90° is,
(x, y) → (-y, x)
By this rule vector will become,
→
If we represent this vector by ,
Then a = -1 and b = -2.5 will be the answer.