Question 9 IfV is solenoidal, then V.V=0 a (x+3y) + (y-2-) + ax a oy (x+2=)...
Question 28 Solve DE: y(4) - 2 y(2) + y = 0 Oy=cieľ + C2 xe* + c3e-* + C4xe Oy=Cix + c2xlnx + c3x-1 + c4 x-1 In x O None of them Oy=cie + C2 X + c3e-* + c4 x-1
Prove Valid: 1. (z)(Pz --> Qz) 2. (Ex) [(Oy • Py) --> (Qy • Ry)] 3. (x) (-Px v Ox) 4. (x) (Ox --> -Rx) ... :. (Ey) (-Py v -Oy) 1. (x) [(Fx v Hx) --> (Gx • Ax)] 2. -(x) (Ax • Gx) ..... :. (Ex) (-Hx v Ax) 1. (x) (Px --> [(Qx • Rx) v Sx)] 2. (y) [(Qy • Ry) --> - Py] 3. (x) (Tx --> -Sx) .... :. (y) (Py --> -Ty)
Solve for the general solution by separation of variables. = 3y . Oy(x) = 232 +C Oy(x) = Cx3 Oy(x) = Cya © y(x) = x3 + ec y(x) = cq at O y(x) = 3x + c
number 2 x + 3y - 9= 0 b) perpendicular on the line 3x + y + 9 = 0 2. Find the area of the triangle with vertices at the points (6, 7),(-4, 4) and (8, -7).
Suppose Cor(X,Y)=1/3 and oy = 403. Let Z=2X +3Y. If Var(Z) = 240, calculate Var(X).
QUESTION 7 Using implicit differentiation to find az ax for x2 + xy -sin(z)-0 y + COSZ-X Х COSZ-X y COS2-X y +Z sinz-X
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2 Question 2 2 pts The differential equation whose general solution is Y=CCos(6x)+C2 Sin (V6 x) y" by 0 Oy -6y=0 y +6y=0 y"+6y'=0 2 pts Question 3 given that y1= x1 is a solution, if we use the reduction of order to solve the ODE 2x2 y + xy - 3y=0 we find that u= AXR+B (Ax512 - Ax+B Axe5124B
Find the volume of the following regions bounded by the planes: a). 3x+8y+8z=9, 3x+8y+8z=9, y=x, x=0, z=0. b). 5x+3y+5z=2, 5x+3y+5z=2, y=x, x=0, z=0.
Question 2 (1 point) Find the slant asymptote x +x-2 2+1 Oy=x-1 O y=x O y=x+1 y=x-2
2. The defl ection a uniform beam with flexual rigidity EI and applied. be load f (x) = cos (x) satisfies the equation 2 y(0) =v'(0) = 0 11' (2)イ(2) =0 Ely(4) (x) = f (x) (a) Evaluate the deflection y (). '/ sin (a 2) dx =--cos (az)+C Hint:"/ cos (ax) dx=-sin (ax) + C, 2. The defl ection a uniform beam with flexual rigidity EI and applied. be load f (x) = cos (x) satisfies the equation 2...