ers.lhstructure.com/courses/331204/discussion_topics/4085999 3.5 Systems of Differential equations i Solve the system i' ( 12 32 ) and sketch the phase portrait. ii Solve the IVP: -5 I 4 -(12) 1, 7(0) = (2) iii Solve the system of differential equations given by -3-1 iv Solve the linear system ′ = I. 2 Q Search x=x-3y y' y= -2x+2y

Find the most general real-valued solution to the linear system of differential equations [1 -2] a. 5 x1(t) -e^(3t) = ci + c2 x2(t) e^(3t)

Check page 48 of the file for a first-order linear differential equation problem. Solve it using integrating factors and provide all steps. Link: [https://drive.google.com/file/d/1RQ 20 ZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing]

Can you find all equilibria of each system of differential equations and use the analytical approach to determine the stability of each equilibrium? dx1/dt= 4x1(1-x1)-2x1x2 dx2/dt= x2(2-x2)-x2

Find the General Solution to the Differential Equation Refer to page 27 of the linked file for the differential equation. Solve the equation using an appropriate method (e.g., separation of variables, integrating factor). Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2ql5dbpVLCS/view? usp=sharing] Provide a clear and step-by-step explanation of your solution.

Please help me solve step by step. Differential equations

How do you solve T"+(a^2)*lamba*t=0? Thank you

Don't worry about the other problems just focus on i. Thank you!

Solve the differential equation: dP 15x4 – 5, Р(-2) — 8 dx P(x)= 3x^5 - 5x + 94 P(x)= 3x^5 + 5x O P(x) = 60x^^3 - 5x + 94 O P(x) = 3x^5 + 94

Transform the given differential equation into an ferential equations. equivalent system of first-order dif- 31" = 2y', and 3" = -2r'