|| y ey-4x d A, R=[0,2]x[0,/8] R 2( e®)-2 AO A O ( e8 + e 8 - 2 BO | 8 T (e + e-8) .co +e-8 e + e .D 00

Q: (D² – 1) y = 8xe" a. y = c1e¯ª + e* (c2 + 2æ – x²) b. y = c1e-® + e (c2 – 2x + 2x²) С. у C. y =…

A: We have to find which of the following option is correct for the given differential equation…

Q: (3 + j4) (1-j) E. If x+jy find x. 4-j5 a. -0.005 b. -0.125 c. -0.454 d. -0.951

A: we know that: j2=11j=-j(a+b)(a-b)=a2-b2

Q: Find T 1 = -1 wwwman x² dx + C

A:

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: 9. Evaluate -2x +9x-1 dx (x² – 2x +1)(x +2) -

A: Solve the problem using partial fractions

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: Se O X + C Evaluate dx 3 2 2 + C + C e О 2х + C

A:

Q: 1 + 19Vx| dx 6x3

A:

Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

A:

Q: Evaluate (4x – 6x +1) dx, where A is a constant and A > -2. -2 O 443 – 6A + 20 O A4 – 3A2 + A - 2 O…

A: To evaluate ∫-2A4x3-6x+1dx

Q: Which of the following is equal to | (x6 – 7x)*dx 1 A (x5 – 7)5 +C - 25 B (x6 – 7x)5 + C - 1 (a6 –…

A:

Q: x+5)(x-2)2 (x-3) Select the Domain of the rational function R(x) a. (-00, -5) U (-5,2) U (2,3) U (3,…

A: To find the domain of the given rational function

Q: Q4 Integrate the following: (a) 4ln|x³| + C x3 dx (b)+C 4 (c)++C (d)+C

A:

Q: 2х + 1 бх2 + 23х — 9 dx х3 + 2х2 — 3х Ja- 2)(x – 3)² dx

A:

Q: 2x+1 10x+5 + dx 2. Show that (* +1)(2-x) x +1 2-x (4x² + 4)(2–x)' . Hence, find

A:

Q: •5 | Vx2 – 9 dx 3

A: Integral formulae: ∫x2-a2=x2x2-a2-a22lnx+x2-a2+C Given integral is: I=∫35x2-9dx Comparing given…

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

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

A:

Q: Find dy for x5 + 2y* = 5y dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable.…

Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

A:

Q: 2(14 – 2)² dx = (14 – x)² dx %3D

A: ∫ x1314-x2dx=∫ 196x13-28x43+x73dx=∫ 196x13dx-∫ 28x43dx+∫ x73dx=147x43-12x73+310x103Add a…

Q: the Pollowing D.E So Ve 3メ 12 X +3 =e |

A:

Q: 2 (3г — 1) V 32? — 2х +3 dx -

A:

Q: 3 2 ²²(4-x²) dy dx = 7 0 true O False

A:

Q: 2. ydx + (3x – xy + 2)dy = 0

A:

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

A:

Q: e2y (е) dy |19+ edy)

A:

Q: x/l+x dx 3.

A:

Q: S (e3 In = + e3) dx = A. 3 + +C B. + 3e3z + C C. + 3e* +C С. 4 D. + +C 4 e3z E. 주 + + C 3

A:

Q: x²+2x Evaluate J x+1)² 17. C. +1+C A.x ++ C x+1 x+1 B. D. + 2x + C + C x+1

A:

Q: (D2 - 3D + 2)y=e5x, Find Y = Yc + Yp O a. O b. O C. O d. C₁e* + C₂e² + 1 2r 12 e -X C₁e + C₂…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.