Find the general solution for the given differential equation y" + 3y' + 2y = 12x2...
3. Find the general solution of the differential equation y” + 2y' + y = 0 (a) y=ce' +c,e* (b) y= ce" + xe * (c) y = cxe* +c,e* (d) y= ce* +C,xe" (e) y=ce?* +c,e-2 (f) y= c,e + ,xe” (g) y=cxe?* +cze 2 (h) y= c,e + ,xe 21
7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.
1.- The given family of solutions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial value problem (a) y = cie" + c2e-, 2€ (-0,00) y" - y = 0, y(0) = 0, 10) = 1 y=cles + cze-, 1€ (-00,00) y" – 3y – 4y = 0, y(0) = 1, y(0) = 2 Cl2 + 2x log(x), t (0, x) ry" – ry'...
Differential Equation Roots rı, 12 General Solution y" - 6y' + 3y = 0 y" + 2y + 5y = 0 Y" +22y + 121y = 0
Find the general solution of the given differential equation. y" + 2y' + y = 14e-t
Find the general solution of the given differential equation y(6) + y" =0 Find the general solution of the given differential equation y''' +3y" + 3y' + y = 0
Ox = C1e3t Find the general solution to the given system. de = 1 = 1 + 2y dy = 2x + y None of these 0x = Cie3t+cze- y=3c1e3+ + cze- y=cie3+ + 3c2e-t -t - Ox 2 = caeht Czert y=-cie3+ + 3c2e-t -t +cze Ox = cie3t y = cie + 3c2e-
The general solution to the differential equation + 2y - 3 y +e-2 y 34 C cos 2 - Ce- y-3- Csin 2x
Question 7 Find the general solution of the given differential equation. y" +2y' +5y=0
8. Find the solution to the differential equation y"+2y'+y=sinx using the method of undetermined coefficients. 1 COS X (a) y=ce' +ce' + -cosx 2 (b) y = ce' +cxe'+ (c) y = cxe' +cze cos x (d) y= c,e* + c xe" COSX 1 (e) y=ce' + ce + sinx 2 (f) y=ce' + exe* + sin x 2 (g) y=cxe' + e*- sinx 2 (h) y=ce' + cxe' 1 sinx 9. Use the method of undetermined coefficients to find...