Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

The solution is .

Step-by-step explanation:

A first order differential equation is called a separable equation if the function can be factored into the product of two functions of and :

where and are continuous functions.

We have the following differential equation

In the given case and .

We divide the equation by and move to the right side:

Next, integrate both sides:

Now, we solve for

We use the initial condition to find the value of C.

Therefore,

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

70 years.

step-by-step explanation: