Engineering
Differential Equations for Engineers
Train on Differential Equations for Engineers with 304 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
Training
Try 5 problems free
Course and path
No account needed for these. The full course is 304 problems for $19 USD a month. What's included
A free account opens the first unit of every course, with hints and solutions.
Preview a course problem
See a problem from Differential Equations for Engineers before you begin.
Course topics
Course topics
Modeling and first-order differential equations
Linear higher-order equations and oscillatory response
Linear systems, eigenstructure, and matrix exponentials
Laplace transforms, discontinuous forcing, and impulses
Nonlinear systems, phase planes, and stability
Boundary-value problems and PDE separation methods
Practice problems
Try a few Differential Equations for Engineers problems, each with a hint.
- A 400-liter tank initially contains 80 liters of brine with 12 kg of dissolved salt Free with an accountModeling and first-order differential equations
- Consider the initial-value problem (x² + 9) y'' + 5x y' − 4y = 0, y(0) = 2, y'(0) = −1 Linear higher-order equations and oscillatory response
- A taut string of length 6 occupies 0 ≤ x ≤ 6 Linear higher-order equations and oscillatory response
- A colony initially contains 800 bacteria and grows at a rate proportional to the square… Linear systems, eigenstructure, and matrix exponentials
- Two masses m₁=m₂=1 lie on a frictionless line and are coupled by three springs of… Laplace transforms, discontinuous forcing, and impulses
- For the weak-competition system x′ = x(4 − x − y), y′ = y(3 − x/2 − y), find and… Laplace transforms, discontinuous forcing, and impulses
- At each of x₀=0,1,-2, classify the point as ordinary, regular singular, or irregular… Nonlinear systems, phase planes, and stability
- In the cube 0<x<π, 0<y<π, 0<z<1, solve u_(xx)+u_(yy)+u_(zz)=0 with zero Dirichlet data… Boundary-value problems and PDE separation methods
- Resolve the startup layer hidden by a quasi-steady sensor model Free with an accountModeling and first-order differential equations
- Reduce a coupled fast–slow subsystem without losing its startup state Linear systems, eigenstructure, and matrix exponentials