(Superposition Principle) Consider (п-1) Any(n) + an-1Y +... + a1y' + aoy = f1(t) + f2(t) +... + fm(t) where an, ...a1, ao E R, and an # 0. Suppose also that y:(t) is a solution to any(n) + an-1y(n-1) + ... + a1y' + aoy = derivative to justify why k1y1(t) + k2Y2(t) + ... + kimYm (t) is a solution to ,(n) fi(t), where 1 < i< m. Use the linearity of the Any (п-1) + an-1y +... + a1y' + aoy = = f1(t)+ f2(t)+... + fm(t), where k1, k2, ., kim E R.

Q: conjugate of v-1-3 is 1- V-1+3 2- -V-1-3 -V-1+ 3 3 - V-1 2- 4-

A:

Q: Exercises(4) 4.1 Select True or False for the following arguments : 1. (PA(p4))H9 2. (Pq)nq)P 3.…

A: The objective is to state whether the following statements are true or false. 1. p∧p→q↦q2.…

Q: (1) IF: ā=21-j+ k, b=i+2j- 3k, č=-3i+2j+ k Find : a.b, ã.č, č.ã‚ (a+b).(a−b),(ã+ê).(ā-č) (a +2b-3c).…

A:

Q: Q2/Let X-N(4,9). Find (a) P(1 2). (c) P(|X-21 >5)

A:

Q: If X(w) 3u-2 find F(z(3t).

A: Note: There is a typo in the choices. To solve this problem, we use the following property.

Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

A:

Q: dQ Find the particular solution of + 4; dt 10+2t Q(2) = 100 2t2+40t+1304 Q а. 2t+10 b. 4t2+40t+1304…

A: Solve by linear differential eq

Q: (2z2 + 2z - 1) - (2z? - 3z + 7) = 5z- 8 O True O False

A: Evaluating the value of the expression

Q: Show that 1 1 1 x2 y? z2 (y² – a²)(z² – a²)(z²? – y²) - - ,4

A:

Q: compute (2A)T − (3B)T

A:

Q: Find the solution of 4x²y" — 4x²y + y = 0, x > 0 of the form Y₁ = x¹(1+c₁x + С₂x² + c3x³ + ...)…

A:

Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

A:

Q: If c (t) = .12t² + 49t +135 gives the number of cars per hour passing through a certain toll both at…

A:

Q: f (x) = Ax + 3, g (x) = Bæ² What are the possible values of A and B if (f o g) (1) 11 ?

A:

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Find the general solution of a = y+2x. O a. y = -z(Inz +c) O b.y = a (2ina +e) O c.y = a(2ina +c) O…

A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey…

A:

Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

A:

Q: Va +3b + Va – 3b If x=- Va+36 – Va– 3b prove that 3bx² – 2ax +3b = 0 | - -

A:

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

A:

Q: Is (1, 19) a solution to ys7x-13 y> 3x+ 6

A: Consider the following equations: y≤7x-13y-7x≤-13                                ...... 1…

Q: 21 - 21 +k).(21- 3j- 7k) = %3D 3/4 1/2 3.

A: Let two vectors, be r1 =a1i^+b1j^+c1k^ and r2 =a2i^+b2j^+c2k^  . The dot product of these vector, r1…

Q: For u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b)…

A:

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3<…

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A:

Q: 1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C)…

A: