2. Find the general solution of the Euler's equation ty" - 3ty' + 3y = 0 3. Find the general solution of the Euler's equation ty" + 7ty' – 7y = 0, t > 0
dy 4. Solve the following differential equation dir = e2r-3y+4 with y(0) = 0.
Exercise 4: (5 points) consider the following differential equation 3y - y Let = f(ty) be the right-hand side of the above equation. a. Compute a/ay. b. Determine and sketch the region in the ty-plane where functions. and array are both continuous C. For the initial condition y(0) = 1 (i.e.to = 0, y = 1), would a unique solution of the equation exist? Explain.
Solve without using laplace 1. 3y" – 8y' – 3y=0 y(0)=10, y'(0)=0
Consider the IVP y'' + 3y' + 3y = (1 − u(t − 4)) with y'(0) = 0 and y(0) = 0. Solve the differential equation, and if possible, provide a graph
Peoblem 3: Solve the following problems Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00 Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00
Solve the initial value problem. y'" – 3y" - y' + 3y = 0; y(0)=5, y'0) = -3. y'(0)=5 The solution is y(t) =
3. (10 points) Solve the following Bernoulli Equation. ty+2y- y = 0 1>0. 4. (10 points) Solve each of the following and tell whether the differential equation is linear or nonlinear. 2 1 y(i)=0
(1 point) Solve the initial value problem ty" - ty' y = 5, y(0) = 5, y'(0) = -1 y =
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8 Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8