


use method of undetermine coefficient to find the general solution day d.c2 +7 dy dc =...
8. Use variation of parameters to find the general solution of the ODE day dy daca da 2y = ce2x
Problem 3: Find a solution to the IVP day d.x2 + dy dc + y = 0, y(0) = y'(0) = 1.
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
Use the elimination method to find a general solution. x(t), y(t) for the given system. · = x + 2y dy = -4x - 3y dt
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
dy 2. Find the general solution of -y+e"y dv -6xy 3. Find the general solution of t dr 4y+9x2 dy dx Find the general solution of бх2e" + 4y. 4. 5. Find the general solution of dr (y +2) dy 5x +4y Find the general solution of dx 8y3 d By'-4x
(24 points) Find the general solution to each of the following differential equations dy a) = e)(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 17y = 0. Is this solution (i) undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
Find a particular solution to the differential equation using the Method of Undetermined Coefficients. dy dy -5 + 2y = x e* dx? dx A solution is Yp(x) =
4. (24 points) Find the general solution to each of the following differential equations dy a) = e-(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 177 = 0. Is this solution (i)undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
Find a particular solution to the differential equation using the Method of Undetermined Coefficients. dPy dy -7 + 2y=x e* dx ox? A solution is yp(x)=