3 If ° ) u(t) where a2 u(t) = ( uz(t) and u1 (t) = B1et + B2e' %3D and uz (t) = Bze' then And find the value of %3D a. a2 = 2 b. a2 = 3 В1, В2, ВЗ C. a2 = 1 d. az = –4

Q: (3) Let 0 = 1234 6789 365 987 in S9 (a) Compute o2 and o (b) Write o as a product of disjoint cycles…

A:

Q: Simplify

A: It is given that,           3y32y22y43.y30 We have to simplify it.

Q: In asynchronous transfer mode (ATM) (a communications protocol used on backbone networks), data are…

A:

Q: y' = y2 - 4

A:

Q: (2x+3) 8. S- (x2 +x+2)2

A: Let's find.

Q: Find y'. cot (1) y = 4 cot O A. O B. -8 csc (*) 4 9 CSC 9

A: Given:; Now,           y'=4cotx9'     =4cotx9'     =-csc2x9x9'      =4-csc2x919     =-49csc2x9

Q: Find y". 1 y = tan(-6x - 3) Select one: 2 A.24sec (-6x - 3) tan(-6x - 3) 2 О В.- 2sec (-6х - 3) С.2…

A:

Q: 2. If f(x)=x² -15 and g(x)= 2x+11, a) find (f °g)(2). b) find (gºg)(-6). c) (g•f)(x).

A:

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

A:

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

A:

Q: y"1 +y1 = 0. У 2- У2 %3D 0.

A:

Q: Find if y = (+3)(x² – + 3). %3D R

A: Given: y=1x2+3x2-1x2+3 To find: dydx.

Q: graph of (x) = x' - 2 is shown in the figure. Find 6 such that if0 2 ]x - 4] 2 8, then IAX) - A. ô =…

A:

Q: 13. Find mzEDC. (9x- 1)° EE C. A (2r + 13) D

A:

Q: Se*dx= бх-3 a. +c -3 Ob. e6x-3 +c -6 e6x-3 -+c 6.

A:

Q: x < 3x + 4 and 4x − 1 ≥ 15. Give your answer in interval notation, and sketch a graph of this…

A: Provided that                                       x&lt; 3x+4      and   4x-1 ≥ 15Take…

Q: y²-6x²y=-9x ; y' at (1,3)

A:

Q: (:' } - 8) zp - Vz(z – 2)

A: We use the difference of cube formula for numerator

Q: 3. Why can you not use the power rule to differentiate y = e*?

A:

Q: x+1 If y 2х — уx then y' will be.

A:

Q: 9. у %3D 4sin' (2xх) 10.у %3D tan? (x3) 11.у %3D sec(-х2 + 3х — 4)3

A: Question 9,Given,          y=4sin32x

Q: 2-у (бх + 2у?)dx dy -2

A: On solving this we will get

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: 2 dr x>1 rVF - 1

A: We will find the integral as following.

Q: 13 5x³ y³ • 2 12 x yt

A: Given:2. 5x23y45 . 2x13 y253. 2a12b236

Q: 96, a0ose -bsine =0 a'simo +baose asimo-baose Then,

A:

Q: Find y'. O A. 2x+ O B. 2x- ОС. 2х+ -| -| |

A: we have y=x+1xx-1x

Q: Find y' and y" for x² + 2xy − 3y² = 41. Simplify. -2x - 2y 2x - 6y y" = help (formulas) y' help…

A: Given query is to find the second derivative of the expression

Q: √√x²+9 dx

A: Give integral is ∫x3x2+94dx

Q: Use the drop down menus to match the expression on the left with its simplified form on the right.…

A: 1. Factorize the terms in the numerator and the denominator and simplify.

Q: Evaluate and simvlify y'. sec 2w y sec 2w + 1

A: Given: y=sec2wsec2w+1

Q: 2. Sx³(a² + x²)° dx ? + x?)% dx

A: Using property of integration,

Q: Evaluate les-). d 3x dx OA (3x³- x?)e3x²-x?-1 O A. ² – x² – 1 OB. O B, e oc (9x² - 2x)e³x³-x? OC.…

A:

Q: Evaluate (tanx * dy/dx) - у %3D а a. y = -a + C(cscx) ОБ. None of the choices О с. у%3-а+ C (cosx) O…

A:

Q: Find the second derivative of each item. 1. y = x° + 3x2+ 4x 1 2. y = 3. y = /(4 – x2) 4x 4. y = x +…

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.