First Order Differential Equations

1.Solvedy / dx=x² + x fory(1)=3.

2.Solve dy / dx=sin(5x)fory(0)=2.

3.Solvedy / dx=1 / (x²1)fory(0)=0.

4.Solvey=y³fory(0)=1.

5.(little harder):Solvey=(y1) (y+1)fory(0)=3.

6.Solvedy / dx=1 / (y+1)fory(0)=0.

7.(harder):Solvey=sinxfory(0)=0,y(0) = 2.

8.A spaceship is traveling at the speed 2t² + 1^km/_s(tis time in seconds). It ispointing directly away from earth and at timet = 0it is 1000 kilometers from earth. How far fromearth is it at one minute from timet = 0?

9.Solvedx / dt=sin(t²) + t,x(0)=20. It is OK to leave your answer as a definiteintegral.

10.Solvedy / dx=e^x + xandy(0)=10.

11.Solvex=1 / x²,x(1)=1.

12.Solvex=1 / cos(x),x(0)= / 2.

13.Sid is in a car traveling at speed10t+70miles per hour away from Las Vegas,wherettis in hours. Att=0the Sid is 10 miles away from Vegas. How far from Vegas is Sid 2hours later?

14.Solvey =y,y(0) = 1, wherennis a positive integer. Hint: You have toconsider different cases.