Solve the separable differential equation: dx/dt= x^2+ (1/9) and find the particular solution satisfying the initial condition: x(0)=6

The particular solution satisfying the initial condition, , of the differential equation is .

Step-by-step explanation:

A separable differential equation is any differential equation that we can write in the following form.

We may find the solutions to certain separable differential equations by separating variables, integrating with respect to x, and ultimately solving the resulting algebraic equation for y.

To find the solution of the differential equation you must:

Separate the differential equation and integrate both sides.

Solving

Therefore,

Now, we use the initial condition to find the value of the constant E.

Thus,

and we solve for x,

y-y1=4(x-x1)

step-by-step explanation:

this is point-slope form since you only have 4 as the slope it goes in place of m

hope this : )

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05