Differential Equation Calculator

Types of Differential Equations

First-Order Linear ODE:

dy/dx + P(x)y = Q(x)

Solution: y = e^(-∫P dx) [∫Q·e^(∫P dx) dx + C]

Separable Equations:

dy/dx = g(x)h(y)

Solution: ∫dy/h(y) = ∫g(x)dx

Examples:

• dy/dx = ky → Solution: y = Ce^(kx)
• dy/dx = x/y → Solution: y² = x² + C
• dy/dx + y = e^x → Solution: y = (x + C)e^(-x)

Common Applications:

• Population growth models
• Radioactive decay
• Newton's law of cooling
• Spring-mass systems