Chapter 1, Problem 8DE

Differential Equations Find the solution to the IVP d^2y/dt^2−5dy/dt+6y=−1e^2t where y(0)=−7,dy/dt(0)=−16.y(t)=

Differential Equations  a)xy'=x^3+4y b) xy'+4y=x^2 c)xy'=3y+x^3

Equations of Order One: Saparation of Variables and Equations with Homogeneous Assignment2.2 S o l v e   t h e   d i f f e r e n t i a l   e q u a t i o n s :

Differential equations. Autonomous systems and stability.Suppose that the solution (x1(t),y1(t)) is defined for all t and that its trajectory has an apparent self-intersection x1(a) = x1(a+p) = x0 y1(a) = y1(a+p) = y0 With p>0. with the solution x2(t) = x1(t+p) y2(t) = y1(t+p) And applying the uniqueness theorem, prove: x1(t+p) = x1(t) y1(t+p) = y1(t) for all t. That is, the solution is closed and has a period p. Consequently the solution to an autonomous system is periodic with a closed path, or never passes through the same point twice. Please be as clear as possible, and legible. Show and explain all the steps in detail and use definitions if necessary. Thank you very much.

Topic: Differential equations Question: Compute for the value of constant (C) by solving the given DE using integrable combination . Let x=3, y=1 2y^2(xdx+ydy)=3(ydx-xdy)