Differential Equation Solver
Differential Equation Solver — Find Solution for dy/dx = f(x,y)
This online differential equation solver helps quickly find solutions to various types of differential equations with step-by-step explanations and graphical visualization.
What is a differential equation?
A differential equation is an equation containing a function and its derivatives. Basic form: dy/dx = f(x,y), where you need to find function y(x).
Types of differential equations
- Separable variables: dy/dx = g(x)h(y)
- Linear equations: dy/dx + P(x)y = Q(x)
- Homogeneous equations: dy/dx = f(y/x)
- Bernoulli equations: dy/dx + P(x)y = Q(x)y^n
Applications of differential equations
- Physics: motion of bodies, oscillations, radioactive decay
- Biology: population growth, epidemic spread
- Economics: growth models, inflation
- Engineering: electrical circuits, heat transfer
- Chemistry: reaction rates, kinetics
How to use the solver?
- Enter the differential equation in standard form
- Choose equation type (or automatic detection)
- Specify initial conditions if needed
- Click "Solve Equation"
- Get general and particular solutions
Examples: dy/dx = 2*x, dy/dx = y, dy/dx = x/y, dy/dx + y = x
Frequently Asked Questions
What is a differential equation?
A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a function changes depending on its current value and variable.
What's the difference between general and particular solutions?
General solution contains arbitrary constants and describes all possible solutions. Particular solution is obtained from general solution when initial conditions are given.
What are initial conditions?
Initial conditions are values of the function and/or its derivatives at a certain point. For example, y(0) = 1 means that when x = 0, function y equals 1.
What types of equations are supported?
Supported: separable variables equations, first-order linear equations, homogeneous equations, some types of Bernoulli equations and other basic forms.
Can I plot the solution graph?
Yes! The calculator automatically plots the solution graph (if possible) and direction field for visual representation of the equation.