Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
X' = ax+b find general solution
Reply to thread
Message
[QUOTE="HallsofIvy, post: 5184246, member: 637751"] I assume you mean that is the solution for the function I called "x1". You still need to find x2 in order to find the vector function solution. Remember that you are solving a "vector differential equation" so you need a function for both components. T=As for "the third term which doesn't have a constant", the set of all solutions to a second order linear [b]homogeneous[/b] differential equation, here [itex]t^2x_1''- tx_1'+ x_1= 0[/itex], form a two dimensional vector space. The two functions, t and t ln(t) are "basis vectors" for that linear space. Every solution can be written as a linear combination of them: c1t+ c2 t ln(t). The set of all solutions to a linear [b]non[/b]-homogeneous equation, [itex]t^2x_1''- tx_1+ x_1= 2t[/itex] form a "linear manifold". Where you can think of a linear [b]vector space[/b], geometrically, as a plane [b]containing the origin[/b] so a "linear manifold" can be thought of as a line or plane that does NOT contain the origin. What we can do with such a set is imagine as using the plane through the origin [b]parallel[/b] to that linear manifold. We can represent a point on that "manifold" as a vector in the "parallel" vector space [b]plus[/b] a vector to that plane. The set of all points (here, functions) in that manifold can be represented as a general function in that parallel two dimensional space [b]plus[/b] that one vector to the plane. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
X' = ax+b find general solution
Back
Top