Differential Equations Answers

verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of denition of each solution. 25. x dy dx 2 3xy 5 1; y 5 e3x # x 1 e23t t d

x(e^y)dy+((x^2)+1dx)/y=0

solve dx/df=3x-4y, dy/dt=x-y

y''+2y'+2y=2 y(0)=0,y'(0)=1

Verify that the given functions form the fundamental set of solution of the differential equation on the given indicated interval.

2x^2y" +5xy' + y = x^2-x

y = C1x^-1/2 + C2x^-1 + 15x^2-1/6x, (-0, infinity)