Linear Differential Equation: Solving for M with Integrating Factor of .5

In summary, the conversation is discussing a linear differential equation with an integrating factor of .5. The final answer is M = 48 + (7e^(.5t)-48)e^(-.5t), but there is some confusion over the value of k and the initial condition. The final answer of 55-48e^(-.5t) is incorrect and needs to be corrected.
  • #1
HerpaDerp
6
0

Homework Statement



dM/dT = .5m-24

I know this is a linear differential equation, with an integrating factor of .5
I get my final answer to be M = 48+ke^(-.5t)

Next, when t = 0, M = 7e^(.5t)...

Giving me k = 7e^(.5t) - 48

so to solve for M..

M = 48 + (7e^(.5t)-48)e^(-.5t)

And finally I get 55-48e^(-.5t)=M which I guess isn't right. Anyone help out what I did wrong here?



My final answer that I get is 55-48e^(-.5t), which I guess is wrong. Where did I go wrong?
 
Physics news on Phys.org
  • #2
The equation is separable. You don't really need an integrating factor. M=48+ke^(-.5t) is close, but you do you get the (-.5) factor in front of the t? That's wrong. And M=7*e^(.5t) at t=0 is kind of an odd way to state an initial condition. Do you mean M=7 at t=0?
 

FAQ: Linear Differential Equation: Solving for M with Integrating Factor of .5

What is linear differentiation?

Linear differentiation is a mathematical process used to find the rate of change of a linear function. It involves finding the slope of a line at a specific point using the derivative of the function.

What are the applications of linear differentiation?

Linear differentiation has many real-world applications, including calculating the velocity of an object in motion, determining the growth rate of a population, and optimizing production processes in economics.

How is linear differentiation different from other types of differentiation?

Linear differentiation is a specific type of differentiation that applies to linear functions, which have a constant rate of change. Other types of differentiation, such as power differentiation, involve functions with changing rates of change.

Can linear differentiation be done by hand or do you need a computer?

Linear differentiation can be done by hand using the rules of differentiation and the properties of linear functions. However, for more complex and detailed calculations, a computer or calculator may be necessary.

What are the common mistakes to avoid when using linear differentiation?

Some common mistakes to avoid when using linear differentiation include forgetting to apply the chain rule, mixing up the order of operations, and making errors in algebraic simplification. It is important to double check all steps and calculations to ensure accuracy.

Similar threads

Simple Linear DiffEq, not understanding the book
Replies
2
Views
986
Finding the Time of Max and 0 Angular Speed
Replies
3
Views
2K
Solving a Puzzling Physics Problem: ##15 \pm 3\sqrt{15}##
Replies
17
Views
2K
How Do You Solve a First Order Differential Equation with an Initial Condition?
Replies
1
Views
2K
Evaluate the Line Integral ∫_{C}xyds for x=t^2 and y=2t, 0≤t≤5
Replies
6
Views
1K
D.E. Linear equation with integrating factor
Replies
4
Views
1K
Solving Arclength of Curve r(t) | Step-by-Step Guide
Replies
2
Views
2K
Solving a mixing problem with a differential equation
Replies
2
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
1K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
940

Hot Threads

Recent Insights

Back
Top