Find the solution of the differential equation that satisfies the given initial condition. xy' + y = y2, y(1) = −5

The solution to the differential equation

given the initial condition  is

Given the differential equation

We can rearrange it as follows:

Factoring the denominators of the LHS, and decomposing into partial fractions, we get

The final rearranged equation is

Integrating both sides;

(We made of a law of logarithms on the last line to simplify the equation)

The initial condition

Substituting into the general solution we got earlier

Substituting the value of back into the general solution

When is made the subject of the formula

Therefore, the solution that satisfies the initial condition is

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Step-by-step explanation:

The given differential equation:

Integrate both sides , we get

At x=1 , y=-5 (given)

Put value of x in (i), we get

hence, the required solution:

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step-by-step explanation:

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step-by-step explanation: