Question

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

Answer 1

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