# Calculators - Differential Equations

## Laplace Transform Calculator

The calculator will try to 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 try to find the Inverse Laplace transform of the given function.

Recall that $\mathcal{L}^{-1}(F(s))$ is such a function $f(t)$ that $\mathcal{L}(f(t))=F(s)$.

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 try to 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.

## Fourth Order Runge-Kutta Method Calculator

The calculator will find the approximate solution of the first-order differential equation using the classical fourth order Runge-Kutta method, with steps shown.

## Half-Life Calculator

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