Given the differential equation (dy/dx)+(2/x)y=x^2y^3 ; solve this equation using the bernoulli method; final answer should be (1/y^2)=?

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Step-by-step explanation:

Given differential equation

Differential equation can be write as

By Bernoulli method

Susbstitute .....{equationI}

Differentiate equation I w.r.t x then we get

Susbstitute the values in the given differential equation then we get

It is first order linear differential equation and compare with the first order linear differential equation

Then we get P(x)= and Q(x)=

Integration factor=

Integration factor=

Integration factor= .

Using

Substitute then we get

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answer: -8.2562234e+13

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!