Question

(1 point) Each graph below represents a solution to one of the following differential equations. Match the graph to the differential equation. (a) " +=0 matches graph 2 (b)" + 4c = 0 matches graph 3 (c)" + 16.0 0 matches graph 4 7 2 3 W (1) (2) (3) (4) -2 -1 (The t-scales on the four graphs are the same.) (d) Find an equation for each of the graphs: For graph (1), z(t) = For graph (2), 2(t) = For graph (3), 2(t) = For graph (4), 3(t) =

Part (d)?

Answer 1

already matched the graphs In bart (a), (bi, a have you with the differential equation, in a similar way , lan differential ear for (1) be given 21" + 9x=0 3 times wore frequency than (2) because it has Now d) for graph (1), 2 - 0+97(x)=0 ' + 9x=0 magnitude is and differential eq" is (According to graph) ot) = C, Cos 36 G K a constant where 2 and magnitude ut --2 Cost (?+9[*] = 0 for graph (2 x + x = 0 Diff. eqh is ata c, cost where c, is a constant (According to graph) and maqnitude from graph is 3. 211) = -3 Lot

for grapa (37, Differential ear is (D?+ 42 [m] =( 49 50 e cos at act (According to graph) Where c, is constant. in graphs is 2 given moqnitude last. 2 Coszt For graße (6), is Differential eqn 20² + 16) (n] =0 O" + 162 = 0 e, sin at acte Constanta Where a in (According to graph) 1 sin 4 t and given magnitude in graph la(t) =