Solve the differential equation dy dx + 12x2y = 36x2. SOLUTION The given equation is linear since it has the form of this equation with P(x) = 12x2 and Q(x) = 36x2. An integration factor is I(x) = e∫12x2 dx = .

Therefore the solution of the differential equation is

   [ where c is arbitrary constant]

Step-by-step explanation:

Given differential equation is

Here   and  

The integrating factor of the differential equation is

Multiplying the integrating factor both sides of the  differential equation

Integrating both sides,

......(1)

Let

putting ,

      [ where c is arbitrary constant]

Putting the value of z

From (1) we get

Therefore the solution of the differential equation is

   [ where c is arbitrary constant]

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.