Question

Is it possible to solve the differential equation

y'(x)= y(x)â|x|


for y(0) = 0? Is this solution unique? Justify.

Answer 1

No, and solutions is is not valid.

Explanation:

Solving y'(x)= y(x)a|x| by parts yields y(x)=
`e^{(a)/(2)x^(2) }` is the solutions, for y(0)=0 (initial value), it yields
`e^(0)=0` which is not valid. Note a is assumed to be constant.