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Separable Differential Equation:
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A separable differential equation is one that can be written in the form dy/dx = f(x)g(y), where the variables can be separated to opposite sides of the equation for integration.
The calculator solves separable initial value problems using the method:
The initial condition y(x₀) = y₀ is then used to determine the constant of integration C.
Process: Separate variables, integrate both sides, apply initial condition to find the particular solution that satisfies y(x₀) = y₀.
Instructions: Enter f(x) and g(y) functions, initial x-value (x₀), and initial y-value (y₀). The calculator will provide the general solution, constant of integration, and particular solution.
Q1: What types of functions can I enter?
A: The calculator supports basic mathematical functions including polynomials, trigonometric, exponential, and logarithmic functions.
Q2: How are the integrals computed?
A: The calculator uses symbolic integration techniques to find antiderivatives of the separated functions.
Q3: What if the equation is not separable?
A: This calculator only works for separable differential equations. Other methods are needed for non-separable equations.
Q4: Can I use this for systems of differential equations?
A: No, this calculator is designed for single separable ordinary differential equations only.
Q5: How accurate are the solutions?
A: The solutions are exact symbolic solutions, not numerical approximations, when possible.