Separable ODE: dy/dx = ky
Solve separable ODE dy/dx = ky with initial condition y(0) = y₀. Evaluate at x.
Interactive Sandbox
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Direct computational model evaluating Separable ODE: dy/dx = ky.
Variable Mechanics
Roles, constraints & impacts
Rate constant k
Rate constant k
Initial condition y(0)
Initial condition y(0)
Evaluate at x
Evaluate at x
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Direct computational model evaluating Separable ODE: dy/dx = ky.
Common Mistakes & Traps
- Ensure all input measurements share consistent units before calculating.
- Check for denominator values approaching zero to prevent undefined division.
- Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).
Dimensional Analysis & Units
Direct evaluation matching formula variable dimensions.
Real-World & Industry Application
Widely utilized across modern calculus applications, academic analysis, and engineering estimations.
Worked Example: Separable ODE: dy/dx = ky
Given:
- k = 2
- y0 = 1
- x = 1
- dy/dx = 2y, y(0)=1
- Separate: dy/y = 2dx
- ln|y| = 2x + C
- y = e^(2x) → at x=1: e² ≈ 7.389
Answer: 7.389
Frequently Asked Questions
What is the Separable ODE: dy/dx = ky formula?
dy/dx = ky → y = C·eᵏˣ. Solve separable ODE dy/dx = ky with initial condition y(0) = y₀. Evaluate at x.
How do I calculate Separable ODE: dy/dx = ky?
Enter Rate constant k (k), Initial condition y(0) (y0), Evaluate at x (x) into the calculator. It applies dy/dx = ky → y = C·eᵏˣ and shows every step of the working.
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