4. Consider the DE 3y' = (y – 1)(1 – 2y). (a) Which of the following is an explicit solution of the DE satisfying the initial condition y(0) = 0? (a) y = (b) y = 글 (c) y = e" -1 (d) y=D . (b) What is the interval of existence for the above explicit solution of the DE ? (a) (In 2, o0) (b) (-0, In 2) (c) (0, ∞) (d) (-∞, ∞) (c) Which of the following is an unstable equilibrium solution of the DE? (a) y = 0 (b) y =} (c) Any function y # 1 (d) Any function y # 1

Q: 1. Find the general solution of y"" — 2y" — y' + 2y = 0

A:

Q: 2. Find the general solution of y" - 2y" - y' + 2y = 0

A: 2. Find the general solution of y'''-2y''-y'+2y=0

Q: 1) Find the Solution. a) (y" - 5 y² + 4y = 0 y(0)=4 5) 4'(0) = 0 " 4" "y" + "y' 4(1) = 5 y' (1)=10 +…

A: We have to find the solution of the given differential equation.Note: According to the guidelines we…

Q: The DE t (t - 3) y" + 3ty - y = 1² has initial conditions y (1) = Yo, y' (1) = Y₁ where Yo and Y₁…

A:

Q: Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x +…

A: Given thatand  are two solutions of DE

Q: Find the general solution to the following: (a) 6y"+y'- y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y'…

A:

Q: 1. Show that y = ze* + e-2* is a solution of y' + 2y = 2e*. 3

A:

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: for the 2nd order nonhomogenous ode y''+4y = 10sin(9pi x t)

A: Given 2nd order non-homogeneous differential equation isWe have to solve the above differential…

Q: 3. (4.2 #3) Find the general solution. y" + 8y + 7y=0

A: The given equation is; y''+8y'+7y=0

Q: If y1 and y2 two solutions of (1 – a²)y" – 2xy' + n(n+1)y = 0; -1<x < 1 Show that W (y1, Y2) : 1-…

A:

Q: 2) Find a general solution for y" + 8y + 16y 0 then find the particular solution for which y(0) = 1…

A:

Q: 3. Find the complete solution of: y" - y' + y = 1 with y(0)=a & y'(0)=ß

A:

Q: 12. At which point A, B, C, D, or E on the graph of y = f(x) are both y' and y" positive? (a) A (b)…

A: Consider the curve

Q: b

A:

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

A:

Q: 5x2y"+ 15xy' + 5y = 0, y(1) = 6, y'(1) = 4. for x > 0. Enter your answer as a symbolic function of…

A: This is a second order Euler homogeneous ODE, use the steps below to solve the problem.

Q: Find a particular solution to y"+ 2y'+ y = 1 (A) (B) y, = 21-1 %3D (C) y,-2r-2 Y, = (D) y, =1 (E)…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.