Lessons
Feeling shaky on the material? Check out a lesson:
Skill Checklist
See everything you need to know in this unit and with an interactive checklist to check your progress.
Speed Run
Improve speed and accuracy with a timed multiple-choice quiz.
Feeling shaky on the material? Check out a lesson:
Feeling shaky on the material? Check out a lesson:
Select a Difficulty
4 / 36 problems visible - Upgrade to view all problems
!!
0 / 7
The curve of y=f(x) is positive definite and satisfies the differential equation dxdy=yex. It is given that f(0)=1.
Use Euler's method with a step length of h=0.5 to estimate the value of f(2).
By solving the differential equation, find f(x).
!
0 / 6
Solve the differential equation dxdy=−yx.
(12,35) lies on this curve, as does (0,a), where a>0.
Find a.
!
0 / 8
A cylindrical oil tank initially contains 256L of oil. Oil leaks from the tank so that the volume V (L) at time t (h) satisfies the differential equation
where k is a positive constant. After 8hrs, there are 16L remaining in the tank.
Show that V(t)=(4−4t)4.
Determine how long it takes for the tank to empty.
0 / 5
Solve the differential equation dxdy=y2x3.
It is given that y(0)=3.
Find y(2).
Ask Plex AI about problem 1
Get hints, ask questions, and work through this problem step by step
