- #1
Mikesgto
- 18
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Homework Statement
11(t+1)dy/dt-7y=28t y(0)=13
Homework Equations
The Attempt at a Solution
I got µ(x)=1/(t+1)^(7/11)
and then used
28/11(t+1)^(7/11)*integral of t/(t+1)^(18/11) dt.
And that's where I'm stuck.
A first order linear differential equation is a mathematical expression that involves the first derivative of a function and can be written in the form y' + P(x)y = Q(x), where P(x) and Q(x) are continuous functions of x. It is called linear because the dependent variable y and its derivative y' appear in a linear form.
To solve a first order linear differential equation, you can use the method of separation of variables, where you separate the variables and integrate both sides of the equation. You can also use the integrating factor method, where you multiply both sides of the equation by an integrating factor to make it easier to solve. Other methods include the method of undetermined coefficients and the method of variation of parameters.
The solution to a first order linear differential equation represents the function that satisfies the given equation. In other words, it is the function that, when differentiated and substituted into the equation, makes the equation true. The solution can also represent the behavior of a physical system described by the differential equation.
Yes, first order linear differential equations have many real-world applications, especially in physics, engineering, and economics. For example, they can be used to model population growth, radioactive decay, and electrical circuits. They are also used in the field of control systems to predict and analyze the behavior of dynamic systems.
Yes, a first order linear differential equation can have infinitely many solutions. This is because the solution to a first order linear differential equation depends on an arbitrary constant, which can take on any value. However, if initial conditions are given, such as a specific value of the dependent variable at a certain point, the solution will be unique.