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OleMash [197]
3 years ago
10

A. Find a general solution of the differential equation dy/dx=y2

Mathematics
1 answer:
wlad13 [49]3 years ago
6 0

Answer:

a) y = - \frac{1}{x+c}

b) y = 0

Step-by-step explanation:

Solution:-

- We are given a ODE of the form:

                                   \frac{dy}{dx} = y^2

- To solve the given ODE and determine the general solution we will separate the variables in the given ODE as follows:

                                  \frac{dy}{y^2} = dx

- Integrate both sides and determine a general explicit function of (y):

                                  \int {y^-^2} \, dy  = \int {} \, dx + c\\\\-\frac{1}{y} =  x + c\\\\y = -\frac{1}{x+c}

b) The singular solution that exist but is not included is the trivial solution corresponding to y = 0. This solution satisfies the the given ODE

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