Answer:
(a) The general solution of given differential equation is .
(b) The unique solution is .
Step-by-step explanation:
(a)
The given differential equation is
Use variable separable method, to solve the above differential equation.
Separate the variables.
Integrate both sides.
The general solution of given differential equation is .
(b)
The given differential equation is
Use variable separable method, to solve the above differential equation.
Separate the variables.
Integrate both sides.
... (1)
It is given that y=1 at t=3. Substitute y=1 and t=3 in the above equation.
Substitute in equation (1).
Therefore the unique solution is .
Answer:
It depends on what operation you are doing
Step-by-step explanation:
in addition its false For Example: -2+(-2)= -4
in subtraction its false For Example -8 - (-2)= -6
in multiplication its true For Example: -8 x -3 = 24
in division its true For Example: -8/-2 = 4
Notice that
(1 - <em>x</em>)⁵ (1 + 1/<em>x</em>)⁵ = ((1 - <em>x</em>) (1 + 1/<em>x</em>))⁵ = (1 - <em>x</em> + 1/<em>x</em> - 1)⁵ = (1/<em>x</em> - <em>x</em>)⁵
Recall the binomial theorem:
Let <em>a</em> = 1/<em>x</em>, <em>b</em> = -<em>x</em>, and <em>n</em> = 5. Then
We get an <em>x</em> ³ term for
2<em>k</em> - 5 = 3 ==> 2<em>k</em> = 8 ==> <em>k</em> = 4
so that the coefficient would be