Question

1) Basic Euler’s Method:

y'+xysin/y+1 y(0)=1

a) What is the initial condition?

b) What order is this differential equation?

c) Is this an autonomous differential equation?

d) Is this a separable differential equation?

e) Find the general solution to the given differential equation, by hand. You will not be able to completely solve for y(x) – that’s ok. Write out all your work and attach it to your Questions tab.

f) Using the initial condition, solve the initial value problem and include this solution in your Questions tab.

Answer 1

a)The initial condition is y(0) = 1
b) 1.The order of the differential equation is the order of highest derivative present in the equation.
c) Yes. Since the differential equation depends on both x, and y. Autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable.
d) No. A first order differential equation y′=f(x,y) is called a separable equation if the function f(x,y) can be factored into the product of two functions of x and y: f(x,y)=p(x)h(y), where p(x) and h(y) are continuous functions. This seperation is not possible here.