# Differential Equations Calculators

## Laplace Transform Calculator

The calculator will find the Laplace Transform of the given function.

Recall that the Laplace transform of a function is $$F(s)=L(f(t))=\int_0^{\infty} e^{-st}f(t)dt$$$. Usually, to find the Laplace Transform of a function, one uses partial fraction decomposition (if needed) and then consults the table of Laplace Transforms. ## Inverse Laplace Transform Calculator The calculator will find the Inverse Laplace Transform of the given function. Recall, that $$\mathcal{L}^{-1}\left(F(s)\right)$$$ is such a function f(t) that $$\mathcal{L}\left(f(t)\right)=F(s)$$\$.

Usually, to find the Inverse Laplace Transform of a function, we use the property of linearity of the Laplace Transform. Just perform partial fraction decomposition (if needed), and then consult the table of Laplace Transforms.

## Wronskian Calculator

The calculator will find the Wronskian of the set of functions, with steps shown. Supports up to 5 functions, 2x2, 3x3, etc.

## Differential Equation Calculator

The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous.

Initial conditions are also supported.

## Euler's Method Calculator

The calculator will find the approximate solution of the first-order differential equation using the Euler's method, with steps shown.

## Improved Euler (Heun's) Method Calculator

The calculator will find the approximate solution of the first-order differential equation using the Improved Euler (Heun's) method, with steps shown.

## Half-Life Calculator

This calculator will calculate the half-life, initial quantity, quantity remained and time, with steps shown.