Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

i need to solve equation

MIT 18.03SC Differential Equations
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

|dw:1351014321172:dw|
|dw:1351014635037:dw|
use equation i cant understand plz

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Here, $$\lambda$$ is a repeated eigenvalue for the linear system $$\frac{d\,\mathbf{X}}{dt} = A\mathbf{X}$$ so if $$\mathbf{X}_1(t) = (\mathbf{w} + t\mathbf{v})e^{\lambda t}$$ satisfies the linear system of equations, then \[ \frac{d\, \mathbf{X}_1}{d t} = \frac{d\, }{dt} \left( (\mathbf{w} + t\mathbf{v})e^{\lambda t} \right) = \frac{d\, }{dt} \left( \mathbf{w}e^{\lambda t} + t\mathbf{v}e^{\lambda t} \right) = \lambda\mathbf{w}e^{\lambda t} + \mathbf{v}e^{\lambda t} + \lambda t \mathbf{v}e^{\lambda t} = A\mathbf{X}_1 \] So, by evaluating the matrix-vector multiplication on the far right hand-side, and factoring, we find \[ e^{\lambda t}(\lambda \mathbf{w} + \mathbf{v}) + te^{\lambda t}(\lambda \mathbf{v}) = A(\mathbf{w} + t\mathbf{v})e^{\lambda t} = e^{\lambda t}(A\mathbf{w}) + te^{\lambda t}(A\mathbf{v}) \] by equating like terms, \[ \lambda \mathbf{w} + \mathbf{v} = A\mathbf{w} \text{ and } \lambda \mathbf{v} = A\mathbf{v}.\] For the first equation we can solve for the desired \[ \mathbf{v} = A\mathbf{w} - \lambda \mathbf{w} = \mathbf{w}(A - \lambda I), \] so \[ \mathbf{v} = \mathbf{w}(A - \lambda I) \] as desired. I hope this helps!

Not the answer you are looking for?

Search for more explanations.

Ask your own question