Math Problem Statement

The function Q(t) satisfies the following ordinary differential equation: dQ/dt = -11Q. What is the general solution of this equation?

Solution

The given differential equation is:

dQdt=−11Q\frac{dQ}{dt} = -11Q

This is a first-order linear ordinary differential equation. To solve it, we can use the method of separation of variables. Let's proceed step-by-step:

  1. Separate the variables: [ \frac{1}{

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Math Problem Analysis

Mathematical Concepts

Ordinary Differential Equations
Separation of Variables

Formulas

dQ/dt = -11Q
Q(t) = Ce^(-11t)

Theorems

Separation of Variables

Suitable Grade Level

College Level

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