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.