WORKSHEET 24
1. Find the first two approximations using Euler’s method for the initial value prob-
lem dy
dx = 2y,y(1) = 2, starting at x= 1 with dx = 0.1.
2. Find the first two approximations using Euler’s method for the initial value prob-
lem dy
dx =y+ 2 cos x,y(1) = 2, starting at x= 1 with dx = 0.1.
3. Find the first two approximations using Euler’s method for the initial value prob-
lem dy
dx =x
y,y(1) = 2, starting at x= 1 with dx = 0.1.
4. Find the solution for the differential equation dy
dx
−y= 1 if y(0) = 3. What is
y(1)?
5. Find the solution for the differential equation dy
dx + 2xy =yif y(0) = 5. What is
y(3)?
6. Solve the above problem using separation of variables.
7. Find the solution for the differential equation dy
dx
−3
x(x−3) y=x−3 if y(4) = 2.
8. Find the general solution of xdy
dx =y+x2
x+1 .
9. Find the solution for the differential equation xdy
dx ln x=x2ln x−yif y(e) = 1
4e2.
10. Find the solution for the differential equation xdy
dx = cos x−yif y(π/2) = 0.
11. Find the solution for the differential equation x2dy
dx
−2yx =x4if y(1) = 0. What
is y(3)?
12. Find the orthogonal trajectories to the family of curves x2
4+y2
9=a.
13. Find the orthogonal trajectories to the family of curves y2= 4ax.
14. Find the orthogonal trajectories to the family of curves exy=a.
15. Find the orthogonal trajectories to the family of curves y=eax.
16. The population of deers in nature is modeled by the differential equation
dP
dt =P(1 −P)
1
