The Answer Is a Function

You'll learnto test a candidate by computing both sides of the equation separately, to see why agreement at one input proves nothing, and to finish an initial value problem by using the point you were given.

Solving an algebraic equation produces a number. Solving a differential equation produces a function, and checking one means doing something you already know how to do: differentiate the candidate, that is the left side; substitute the candidate wherever y appears, that is the right side; then ask whether the two are the same expression, for every value of the variable. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · BOTH SIDES, EVERY INPUT, EVERY GIVEN FACT · v2

Differentiate one side, substitute the other, then compare

Before you start

What you're looking at

Two boxes, one for each side of the equation. The left box differentiates the candidate; the right box substitutes it. A teal line underneath says whether they agree.

The question

Do the two sides come out as the same expression — and if a point was supplied as well, does the candidate pass through it?

Step 1 / 12