Differential Equations

Let y:(- , ) (0, ) be the solution of the differential equation dydx= e5xy3+y3ex+exy4, satisfying y(0)= 1 2. Then the value of y( e 2) is

1. 5+ 352
2. 7+ 532
3. 7+ 532
4. 5+ 352

Let f(x) be a continuously differentiable function on the interval (0, ) such that f(1)=2 and t x t10f(x)-x10f(t)t9-x9=1 for each x>0. Then, for all x>0, f(x) is equal to

1. 3111x- 911x10
2. 911x+ 1311x10
3. -911x+ 3111x10
4. 1311x+ 911x10