5y" - 16y = -8y' Determine the Characteristic Equation for the given Differential Equation. A 5R2 - 16 = 0 B 5R3 + 8R3 16R = 0 c 5R2 + 8R - 16 = 0 D 5R2 - 16R - 8 (E 5R2 - 16R +8 = 0 F 5R2 + 8R 16y = 0

Form the differential equation if its solution is y = acos2x+bsin2x a. y +4y=0 of b. y" – 4y= 0 C. y +2y=0 d. y +2y=0

The indicial equation for the differential equation y"+7y'- 5xy = 0 is O A (r + 7) = 0 %3D O B. (7r - 1) = 0 Oc r-6) = 0 OD (7r + 1) = 0 O E. (* + 6) = 0

Find the solution of the differential equation 2x3 – 9x2 + 6x y" – 3y' + 2y = %3D y = C,e* + C,e2* + x³ + x a. %3D b. y = C,ex + C,e2x – x³. y = C,e* + C,e²x + x³ с. %3D d. y = C, e* + C2e2x + x³ – x %3D

Solve the differential equation using Separable of variables.

Which one of the folowing is the Exact differential equation? (x2 + 3xy)dy+ (y³ +a²)dx = 0 3 %3D (x² +3xy)dx + (y°+ 3 x²)dy = 0 3 (x2 +3xy)dx + (y + *)dy = 0 O (x2 +3ay)dy + (y³ + a³)dx = 0 %3D difforontinl eguation ?

Form a differential equation by eliminating the arbitrary constant a and b from the equation y = ax² 2bx

Solve the Differential Equations by Inspection (40xy-21y*)dx – (35xy³-20x²+20x?y-14xy*)dy=D

Which of the following systems of differential equations would dictate the rates of change of the salt concentration for the two-tank system shown below? 10 L/min 70 g/L VAL 14 L/min I 6 L/min OC A/= (1/VA) (10 × 70 + 6cg - 14CA), c_l= (1/V₂) (14c. – 16c) OC Al= (1/VA) (70 – 6cв - 14CA), CB= (1/VB) (14CA - 16CB) 16св) VB L C Al= (1/VA) (14CA CB/= (1/VB) (14CA - 16CB) 10 × 70 – 6cß), C Al= (1/VA) (10 × 70+ 16cB - 14CA), CB/= (1/VB) (14CA 10CB) 10 L/min