(D² - 3D + 2)y=e5x, Find Y = Yc + Yp a. 1 0² C²²² +₂²³ +2² Cet C 2 2x 5x 12 O b. O C. O d. Ce + Ce 2 Се -X e, none 2x -C₁et - C₂e² + -2x -X - ce е + -2x + 1 12 1 12 1 e 5x e St 12 - 5x e - 5x

Q: Integrate the given expression. [(4x + 2)2 dx A 16 x 3 + 8x 2 + 4x + C 3 B) 32x+ 16 + C (c) 16x 3 +…

A: ∫4x+22dx =∫16x2+4+16xdx =16x33+4x+8x2+c

Q: In ABCD, mZB = (4x – 14)°, m2C m/D = (6x + 8)°. What is the value of ? x – 1)°, and -

A:

Q: Find -2 (4x3 + 12x² - 2)dx

A: Evaluate the difite inetegral: Formula used:

Q: 2. obtain the general solution. a.(D² – 3D + 2)y 2x- 9x + 6x. b.(D + 4)y = 5e - 4x. c. (D² + 4)y = 5…

A: (b).   The given differential equation is: (D2+4)y=5ex-4x

Q: iv) (x+ yi)(3i + 2) = (2x – 3y) + (3x + 2y)i %3D

A: The detailed solution is given below Thank you

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

A:

Q: B S x4+5x³-6x² +18 x³ + 3x² dx.

A:

Q: Given the universal set U = {x|xel, -10 <x<10 } A = {-2, -1, 0, 1, 2, 3 } B = { 2, 3, 4, 5, 6, 7} C=…

A:

Q: g(x.y)-xn (x-y), as(-2,3) Pind vg ?

A: Given the given function is gx,y=xlnx+y,    x,y=-2,3. Apply gradient formula ∇f=∂f∂xi+∂f∂yj

Q: Q10. Im(iz) = a. Re(iz) b.-Re(z) iz+(-iz) C. d. Re(z) 2

A:

Q: Determine |z| if z =2−3i.

A: z = x +i*y |z| = √(x2 + y2)

Q: (x* + 1) (x²-2x ti>

A: Given  I=∫dxx2+1x2-2x+1 Apply partial fraction decomposition 1x2+1x2-2x+1=Ax+Bx2+1+Cx+Dx2-2x+1…

Q: 14) dx कर Vx2 - 8x - 9

A: Question - Evaluate the integral.

Q: B|a- Find u.v and v xu if u=i+2j-k and v=-2i+2j+2k

A: We have to solve given problem:

Q: ta = -j- 4k and b = - 4i +43 - k. Find 3ā b.

A: TOPIC:- VECTOR ALGEBRA

Q: If v = 7i + 3j and w = 4i - 5j, find 6v - 3w.

A: Given v=7i+3j and w=4i-5j We have to find 6v-3w. 6v-3w=67i+3j-34i-5j=42i+18j-12i+15j=30i+33j

Q: Solve by the addition method: 5x 4 3. 3. 2х у 11 3 2 6. II

A:

Q: S(x² – 2),Wxdx = 2 4 B 2 4 D

A: We have to solve the given integration.

Q: Let à = 27 - 5j + 4k and b = − − 5j + 4k. Find -a + b. -ā +b =

A:

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

A:

Q: 2 d) ²₂t(t4 +3t)dt -2

A: We need to solve ∫-22t(t4+3t)dt

Q: Determine Proy,b si ā = 3i– 4j+2k y b = -2i+3j-k

A:

Q: x²y+ 2xy = x + y ise y =?

A:

Q: If Ax) = (x – 5)* thenf(x) equals A x-5e х — 10е 2r D 2r + 25 E 2х — 10е

A:

Q: 2x3- x² + x + 2 dx = D dx find A+B+ C+D. + x+1 + Consider x4 + x3 4 O 3 O 2 O 5

A:

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

A:

Q: 2. Evaluate S 3e +9x2 dx. √√x3e-5 finish early, YOU MUST U

A: Let,u=x³+ex-5 Taking first derivative of u with respect to x,dxdu​=dxd(x3+ex−5)​…

Q: 3 + бх + 5) dx Find 26 + C

A:

Q: If y x4x+3, then 2ix+3ix3 2i 3ix3 O (4x+1)/4x+3 2Ax+3 2x vi3Ar3

A: The function is given by,

Q: If a 10î + 10f + 5k, b = 5i – 2j – 14k, è = 4î + 7j – 4k , find the value of å x (b x 2).

A: The cross product of two vectors a=a1i+a2j+a3k ,b=b1i+b2j+b3k can be calculated using determinant…

Q: 42 x2 dx =. V(73 + 14) 42 / (x3 + 14)+ C V 28 V (x3 + 14) + C 14 (x3 + 14) + C 84 / (x3 + 14) + C

A: From the basic integration