Use euler's method with step size 0.2 to estimate y(2), where y(x) is the solution of the initial-value problem y' = 2 − 3xy, y(1) = 0. (round your answer to four decimal places.)

Step-by-step explanation:

We are given that

Step size=0.2

Initial value problem

y'=2-3xy

f(x,y)=2-3xy

y(1)=0

We have to find the value of

Euler's method of approximation

We have

Substitute the value then we get when n=1

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step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!