Differential Equations: Initial Value Problems Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

CalculusAnswer key includedPDF · Print

Open in generator Start with an easy sheet

Easy: dy/dx is linear

Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

When dy/dx is given as a function of x, integrate it to get y = F(x) + C, a whole family of solutions. The initial condition picks out one of them: substitute the given x and y values and solve for C.

Easydy/dx is linear Mediumdy/dx is quadratic HardInitial conditions away from x = 0

How to solve it: a worked example

Solve the differential equation with the given initial condition.

Start
Integrate both sides
Use the initial condition
Then
Answer

Common mistakes to watch for

Forgetting + C before using the initial condition.
Substituting the initial condition into dy/dx instead of into y.
Solving for C with the wrong sign.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

FAQ

What does the initial condition do?

It picks out one function from the family y = F(x) + C by fixing the value of C.

How do you check the solution?

Differentiate it to make sure you get back dy/dx, and substitute the initial x to make sure you get the given y.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix differential equations: initial value problems with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.

FAQ