The variables x and y satisfy the differential equation dy/dx= xe^x+y. It is given that y = 0 when x = 0. (i) Solve the differential equation, obtaining y in terms of x.

(ii) Explain why x can only take values that are less than 1.

Rewrite the ODE

as

Divide both sides by :

The left side condenses to the derivative of a product:

Integrate both sides and solve for :

Given that when , we find

so that the solution is

I'm not sure I understand the claim that must be less than 1...

sounds & other waves originate from any vibrating object

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2