Match the solution curve with one of the differential equations. y" + 2y' + 2y = 0 o y" + 2y' + y = 0 o y" + 4y = 0 o y" - 2y' - 3y = 0 y" – 4y' + 3y = 0 y" + y = 0 Explain your reasoning. (Assume that k, k,, and k, are all positive.) The differential equation should have the form y" + ky = 0 where k = 2, so that the period of the solution is r. The auxiliary equation should have a repeated negative root, so that the solution has the form c,e -kx + C2xe -kx The auxiliary equation should have two positive roots, so that the solution has the form c,eki* + c,eK2X. The auxiliary equation should have one positive and one negative root, so that the solution has the form c, ek1x + Cze¬k2x. The differential equation should have the form y" + ky = 0 where k = 1, so that the period of the solution is 2z. The auxiliary equation should have a pair of complex roots a ± ßi where a < 0, so that the solution has the form eax(c, cos(ßx) + c, sin(ßx)).

Q: 4. Find a general solution of the differential equation z"-3x + 2x=c² sin

Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

Q: Determine the form of a particular solution for the differential equation. Do not solve. y" -y=tet +…

Q: PFor the differential equations below, write in standard form, and name the type of equation. Then…

Q: Consider the differential equation: y = 3y - 2x Using a pencil, graph the isoclines. Also, using a…

Q: (d) Find an equation for each of the graphs: For graph (1), x(t) = For graph (2), x(t) = = For graph…

Q: differential equation y = C, sin(5x + C2) as its general solution. a) Oy" – 25y = 0 b) Oy" + 25y = 0…

Q: Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1…

Q: Match the solution curve with one of the differential equations. O y" - 2y' – 3y = 0 y" + 2y' + y =…