Question: In Problems 31-40, solve the initial value problem.
The solution of the given equation is .
Evaluate the given equation.
Since, the given equation is the Bernoulli equation with n = -1, and Q ( x ) = x.
Now divide y-1 on both sides of the equation (1).
Let us take u = y2 and . Then,
Find the value of .
Multiply in equation (3) on both sides.
Now integrate the equation on both sides.
So, the solution is found.
Given that, y ( 1 ) = -4.
Then, x = 1 and y = -4.
Substitute the value in equation (4) to get the value of C.
Substitute the value of C in equation (2).
So, the solution is
Question: Riccati Equation. An equation of the form (18) is called a generalized Riccati equation.
use the result of part (a) to find all the other solutions to this equation. (The particular solution can be found by inspection or by using a Taylor series method; see Section 8.1.)
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