Question

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

b. Find a singular solution that is not included in the general solution.
c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b

Answer 1

a)
`y = - (1)/(x+c)`

b) y = 0

Explanation:

Solution:-

- We are given a ODE of the form:

`(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:

`(dy)/(y^2) = dx`

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

`\int {y^-^2} \, dy = \int {} \, dx + c\\\\-(1)/(y) = x + c\\\\y = -(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