Differential equations are at the heart of understanding dynamic systems in fields ranging from physics to biology. With Moogle Math‘s Differential Equations Solver, you can tackle these challenges step-by-step with accuracy and confidence.
Moogle’s Differential Equations Solver helps you:
Solve Ordinary Differential Equations (ODEs)
Example: Solve the equation \( y’ + 3y = 6 \). ‘
Input: solve_ode(equation="y' + 3y = 6")
Work with Initial Value Problems (IVPs)
Example: Solve \( y” + 2y’ + y = 0 \) with \( y(0) = 1, y'(0) = 0 \).
Input: solve_ivp(equation="y'' + 2y' + y = 0", initial_conditions={"y(0)": 1, "y'(0)": 0})
Tackle Systems of Equations
Example: Solve \( x’ = x + y, y’ = x – y \).
Input: solve_system(equations=["x' = x + y", "y' = x - y"])
Analyze Partial Differential Equations (PDEs)
Example: Solve \( u_t = u_{xx} \) (heat equation).
Input: solve_pde(equation="u_t = u_xx")
Visualize Solutions
Example: Plot the solution to \( y’ = 2y, y(0) = 3 \).
Input: plot_solution(equation="y' = 2y", initial_conditions={"y(0)": 3})
Laplace and Fourier Transforms
Example: Find the Laplace transform of \( f(t) = e^{-3t} \).
Input: laplace_transform(function="e^-3t")
To get the best results from Moogle, follow these tips
Example: Solve \( y’ + 3y = 6 \).
Input: solve_ode(equation="y' + 5y = sin(x)")
Example: Solve \( y” – 3y’ + 2y = 0 \) with \( y(0) = 2, y'(0) = 1 \).
Input: solve_ivp(equation="y'' - 3y' + 2y = 0", initial_conditions={"y(0)": 2, "y'(0)": 1})
Example: Solve \( dx/dt = 2x + y, dy/dt = -x + 3y \). .
Input: solve_system(equations=["dx/dt = 2x + y", "dy/dt = -x + 3y"])
Example: Numerically solve \( y’ = y^2 – x^2, y(0) = 1 \).
numerical_solve(equation="y' = y^2 - x^2", initial_conditions={"y(0)": 1})