12- Let Mx,y (t₁, t₂) = e4t+t₁t₂+8t. Then var (Y) is (a) 13 (b) 7 (c) 16 (d) 9

Q: | (3z + 4) dy 2.

A:

Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)

A: Solution :

Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

A:

Q: 10. (D² – 6D + 9)y = e3x

A: Given, D2-6D+9y=e3x To solve the above differential equation.

Q: Q/IF it was AY ₁2) = -12 Y(2) ℗ Y³ (2) = − 12 ⒸY² (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13…

A: Given

Q: (34)-(D+D2)z3 x + y

A:

Q: Maximize B=xy2​, where x and y are positive numbers such that x+y2=10.

A:

Q: - 3t -6t + 6' t2-3'-t3 - 4 -6 -6t2 - Let 7(t) = %3D | Find 7 (t) 7' (t) =

A: We have to find the derivative of the vector function

Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

A:

Q: 2. - q + (q Ap) ~q (q p) T F F T F F 2

A: We have to find the truth table for given statement.

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: 17 (4D? + 4D + 1)y = 0

A: It is differential equation problem

Q: 7. (D² + D²)z = a²y²

A:

Q: . Show that y x2 2 (xyz)(x – y)(y – z)(z - x) N N

A:

Q: (#10) S V4x2+9 dx x4

A:

Q: (D3 + 7D2 + 19D + 13)y = 0

A:

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: 16. (T/F) If A and B are 3 x 3 and B = [b₁ b2 b3], then AB [Ab₁ + Ab₂ + Ab3]. =

A: Given: A and B are  3×3 and let AB=Ab1+Ab2+Ab. To Find: Whether the following statement is true or…

Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: 21 (D² +6D² + 12D+8)) = 0 [AD: y = (C₁+C₂K+ (3²²) ²24

A: Given differential equation D3+6D2+12D+8y=0. The objective is to solve the differential equation.

Q: 2. (D³ – D)y = -2(1+x) + 4e* – 6e¬× + 96e3x

A:

Q: 22. (D³ + 7D² + 19D + 13)y = 0 ; y = 0, Dy = 2, D²y = −12 when x = 0

A: see below the answer and calculation

Q: Evaluate: (8t3 – 9t2 + 7)dt -

A: Topic = Integration

Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Pind Parckial Fraction S+ 2un

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: Vx (x+2) dx = (A) 국2+4 (B) r2+2 + C (0) 등(금2+ 2x)+C (D) ++C 3/2 +x3/2. 3 x (2 5 1 -+ C

A: Given, ∫xx+2dx  We have to integrate it .

Q: Find с dz 23 (2+4) > where C: 13+21=3.

A:

Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

A:

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A: