13. (4a).a 14. (3xy)?. (-4x³y²) 15. (4a b°c®) (2x424-4 -x, 6H03 a Y 6407 16. 3d 6a b? 17. 32xy 4ab 18. 3-X 3d 18 -8.xyz V. 26' a=4 2-Y

Q: Q1/ If y" + 2y' F 5y = e-Sint, y(0) = 0, y'(0) = 1 9=41²^² + (2

A: As per bartleby guidelines we only give first question answers.  Let's solve given diffrential…

Q: Q4:- Find sinvx dx n=5 by trapezoidal and Simpson method.

A: Given integral is   n=5 Here f(x)=sinx By Trapezoidal rule…

Q: Find Duf at P. 3 f (x, y) = sin(3x – 5y); P(5,3); - - NOTE: Enter the exact answer. Duf =

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Q: Solve for the general solution of (D² - 1)y = sinx using variation of parameters

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

A:

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: pol DA 4. x dy + y dx = 0 (3x²y² + 2y³ - 4y) dx + (2x³y + 6xy² - 4x) dy = 0

A:

Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

A:

Q: dx S (x² – 6x + 13)² 4.

A:

Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

A:

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: find dy/dx 3x² +5y'x² +4/y, a) x² +4x,/y-5y² = 3 (ans.: 2x 10x'y- Jy

A:

Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: #5 ở V - (2xy sinz) - (3y~); + (5x> y? z?)k .* and vx ů. ealeulate

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Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: 1. Solve, using the method of variation of parameters: y" + y = sec 0 tan 0

A:

Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: dy y dx 2x = 3y2 – 2 when y = 1 and x = 1 in terms of x. %3D - -

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Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

A:

Q: 4x-6z+5 2+3cosz sin z 9. Find dz.

A: Here we have to integrate the given Integral.

Q: 7T 2 Find 35 cos(7x) dx 5π 2 7T 2 35 35 cos(7x) dx = -5π လ

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Q: L sinh-t %3D .a 3s2-4 6. .b O 9s2 -4 .c O s2-4 3. .d O 2s2-4

A: We know that  L( sinh(a)t) = (a)/(s^2 - a^2)

Q: y" + 4y = 2 sin(6x)+ 6x²e¬3z + 5x,

A:

Q: Can you help me step by step?

A: The derivative of a function is computed as follows.

Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

A:

Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

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Q: y 3D 1 y = secxtanx; y

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Q: 17 (7+ x²^ dy when y = dx Find %3| 7 – x²

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Q: Q2. Solve yfrcos (4) + ysin (2)] dx – x [ysin (2) – xcos (2)] dy = 0

A: Here we have to solve the above differential equation  by first checking whether the function is…

Q: (D² – 2D + 1)y = 2sinx 2 Yp= Ур = 2sinx · Yp = = COSX Ур 3 Sinx- 2cosx Yp = sinx+ COSX

A: I have used the rule for finding particular solution and find that  Option (B) is correct.

Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: 13. If y=(x 2+6)7​, find d 2y/dx 2. d 2y/dx 2=?

A: We have given y = x2+67 Differentiating with respect to x  dydx=ddxx2+67 dydx= 7x2+67-1 ddxx2+6…

Q: d?x + 4x = sin2t Q5: Solve: %3D dt2 Using variation of parameters method?

A: Answer

Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

A:

Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: b) dr cos² #√5 + tanz c) ₁ dt (3-5t)²

A:

Q: In order to evaluate x dx V4x2 we use the 9. substitution 3 sec 0 O x = 3 sec O 9. sec 0 4 4 = x sec…

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Q: 3z (sec-(-3z?))³ 2|–3z*|-/9zª–1 If y= sec-1 (-3x²), then dy dz

A:

Q: Find Duf at P. 3 4 f (x, y) = sin(x – 5y); Р(5, 1); u = i и %3 - - NOTE: Enter the exact answer. Duf

A: This is a directional derivative problem

Q: sin(3z+z²) Find y' for y = (6 – 2*)3

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Q: * 2e² + 6z² – 8z + 6 cosh 3z dz ez + z3 – 2z2 + sinh 3z |

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Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: 5) SOLVE dy _ yz %3D x2

A: A differential equation is an equation in x,y and derivatives of y. An ordinary differential…

Q: 1 dz -÷z³ = t² + 3t – 2 dt 3 z2 -

A: Differential equations and their type

Q: 14. Find dy if y = sec(x² – 1). |

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.