Solve the equation by using Bernoulli's equations. y' + p(x)y = f(x) y

djeljenike

djeljenike

Answered question

2021-09-15

Solve the equation by using Bernoullis

Answer & Explanation

Nichole Watt

Nichole Watt

Skilled2021-09-16Added 100 answers

Step 1
Y+p(x)y=f(x)ylny
divide equation with y both side we get

y/y+p(x)=f(x)lny

now consider lny=t

1ydydx=dtdx

dtdx+p(x)=f(x)t

Step 2

Now apply integrating factor type to solve differential equation

dtdxf(x)t=p(x)

I.F=eF(x)dx

solution of given equation

t×I.F=p(x)I.Fdx+C

|ny.I.F=p(x)I.Fdx+c​​​​​​​

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