Find the function whose derivative is three times itself and whose value at zero is two.

Vault Of Euclid

Solving a Simple First-Order Differential Equation

Recurrences warmup

Solve the equation $Df = 3f$ if $f(0) = 2$.

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

derivatives of exponential functions
the chain rule
evaluating functions at a point

What this problem tests

Tests the ability to recognize the exponential function as the solution to a proportional growth differential equation and to apply an initial condition.

This type of problem introduces the concept of differential equations, often serving as a bridge between basic calculus and more advanced topics like generating functions or continuous growth models.

Solving a Simple First-Order Differential Equation

What you need first

What this problem tests

More on Recurrences