Solve the given equation. Find y as an explicit function of x, if possible 2y' y2-1...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' + 2y' + y = 0; y1 = xe−x y2 =
Solve the given differential equation by undetermined coefficients. y'' − 2y' + 2y = e^2x(cos(x) − 8 sin(x))
1. (3pts) Find the general solution for the equation 2xy + y (No y' 4y4 + y2 need to write your solution in the explicit form.) 2. (3pts) Find the general solution of 2,4 = Express the general solution in the explicit form. 3. (4pts) Find the solution of the given initial value problem in explicit form: 3x2 2y – 3 1 y' =
1. (4 points) Determine whether the given function y, given explicit or implicit, is a solution to the corresponding differential equation a) y = 2* +3e2a; y" - 3y + 2y = 0. dy 2.ry b) y - In y = r2+1, (Use implicit differentiation) dr y-1 2. (3 points) Find the solution to the initial value problem: dy = e(t+1); y(2) = 0 dr 3. (3 points) Find the general solution to the following equation. y dy ada COS
Find an explicit solution to the given differential equation. 1 + (x/y- sin yly = 0
Find the solution of the given initial value problem in explicit form. y′=(9x)/(y+x^2y), y(0)=−3 Enclose arguments of functions in parentheses. For example, sin(2x).
4. Solve the differential equation by parameter variation. 2y" + y - y = x + 1 Please try to write as clear as possible I will be very grateful
1) y'' -2y'+y=xE^x, y(0)=y'(0)=0 Solve the initial value problem using the Laplace transform. y" – 2y + y = xe*, y(0) = y'(0) =
LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions by solving the equation for y in terms of x. (positive function) X Y2 = (negative function) Y V
Find an explicit solution of the given initial-value problem. ✓ 3 ✓ 1 - y2 dx - V1 - x? dy = 0, y(O) = 2