Find the general solution (implicit if necessary, explicit if convenient) for the following: 2 dx
Find the general solutions (implicitly if necessary, explicitly if convenient) of the separable differential equations. dy/dx = ysinx
1. Determine the solution to the following differential equation (implicit if necessary): 2. Determine the general solution, y(x), to the following differential equations [use synthetic division to solve a), b), and d)]. Show all your work dx3dx2 dx b)@y-4ーー3을y+18y = 0 d2 dx2 dx3 dx dx2 dx + 2-10 dy, dy _ y = 0 dx dx x f) χ +dy=kx where k is a constant dx2 dx
d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the form F(x)GK, in which the coefficient of x2 is 84. Answer: =K e. Find the particular solution of the differential equation (4 +x2)으-2V 16-r, such that y-t as x →-2. dx Simplify your answer as much as possible. Answer: y= d. Find the general solution of the differential equation56-48x + 49y - 42xy dx Give an implicit solution in the...
Find an implicit and an explicit solution of the given initial-value problem. (Use x for x(t).) dx 4(x2 + 1), (3/4) = 1 dt implicit tan?(x) = 4t+ 311 4. X
[H] Consider the differential equation dx 1+x2 (H.1) Find the general solution of the above differential equation. You may leave your answer in implicit form for this part. (H.2) Find the particular solution of the above differential equation satisfying y(0) = - Write your answer in EXPLICIT form [i.e. y = f(x)].
both please 1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy dy 2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx X by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. 0
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 the general solution or particular solution of each the following DE's 1) (y-y2 tanx)dx + (2y+tanx)dy=0 2) (x2+y2+x)dx + xydy-0 i y(-1)-1 4) For the initial value problem y' + xy - xy? ex2 ; y(0)-1 Find the explicit solution if y>0 dy dae dy
cos y 1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy cosydy - x CSC²y dy xoschy cosy Xcsc²y.t dx cosy dy = xoscay.secy dx
2.rezy (15 points) Consider the first order separable equation y An implicit general solution can be written in the form ey +C Find an explicit solution of the initial value problem y(0) = 1 y=