x°y + x*y – y = 2x*

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: r5TT T Show that fi (x) = e* , f2(x) = sin x are 4 '4

A: Use standard innerproduct of L2 space

Q: 4. Test whether the following ODE is an exact DE then solve it. (- 3y2 + x) dx + (Inx – 6xy)dy = 0 ;…

A:

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: consider the ODE y'=2y/x, y(x0)=y0 does it have a solutioon for i. x0=0 and y0/=0…

A: @

Q: V. Let z be a function of r and y, and tan y2 + x2 = z*ey. Solve for dz dz and

A:

Q: 5. Solve the following ODE using Fourth-order Runge-Kutta Methode to find y(1.00) if y(0)=-1,…

A:

Q: Prove that the following ODE is exact and find the general solution dy (2xy + 1) + (x² + 3y²) dx

A:

Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

A:

Q: Use there solue the IVP 2. of xZ dn - 24y cO g (6) = -4 y'Co) = t 4 y Cx) =

A:

Q: Solve the following ODE using separable variable method: +(x-3)y = 0. dx a) dy (r+4) b) dr x(y +4)…

A: We can solve the given ODE's as below by separating the variables as below.

Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

A:

Q: The ODE dx dy (x+y +5) is separable. %3D Select one: O True O False

A:

Q: Classify the ODE's according to their linearity. Write th solutions. (e cosxxy)dx 1 dy _ 1 ii) y4 dx…

A: Rearrange the ODE, 1y4dydx-1xy3=x by multiplying both sides by y4 and obtain dydx-yx=xy4. The…

Q: 9 Floy : 2vin8t y co)= 2

A:

Q: Solve the following ODE by Heun's method, y'(t) = y -Jy sint, 2<t< 3, y(2) = 2, h=0.5

A: The differential equation is y't=y2-ysin t where 2&lt;t&lt;3, y2=2,h=0.5. By Heun's method,…

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: A second order ODE has the following solution y(x) = ex (C, cos (3x) + C2 sin (3x)) What's the ODE…

A:

Q: 5. By making a suitable substitution, find the general solution y= y(r) of the ODE dy = (y – 4r –…

A:

Q: The function y=4 sin z satisfies the IVP: %3D y" +y = 0, y(7) = 0, y (7) = -4. Select one: O True O…

A:

Q: Solve the PDE u + 2xtu,=u²; *ER,t> 0 by reducing it to an ODE using an appropriate choice of…

A: As per the question we are given the following first order PDE : ut + 2xtut = u2  ,  x ∈ R , t &gt;…

Q: 3. Show that the following ODE is homogeneous then solve it. 2xyy' = x2 + y?

A: 3). Given: 2xyy'=x2+y2 So, we can also write as: 2xydydx=x2+y2dydx=x2+y22xy....1 Let,…

Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: dw Use the Chain Rule to find , where w = sin 8x cos 4y, x= dt , and y = t. dw dt (Type an…

A: Given w= sin(8x)cos(4y), x=t/2 , y=t3

Q: This is homogenous ODE dy_ (2xy² + yx³) (r' + y') dx Select one: True False II

A: ODE is homogenous if     f(x,y) = λ⁰ f(x,y)

Q: Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

A:

Q: (b) (sin 0)y"+ (0+ cos 0)y" 2tan@

A: Given: sin θy'''+θ+cos θy''=2 tan θ (a) The number of the highest derivative in a differential…

Q: O i using The( 3) uence Xm>is

A: First we have to show that Given sequence is monotonic and bounded then it is convergent

Q: Use the D-Operator method to solve the following ODE: d y +4y= 2 sin 2.x dx²

A: To obtain the solution, use the following formulae. ddx=Dd2dx2=D2 The particular integral of the…

Q: For the ODE below, assume that p > 0 is a constant. dy = P – e U dt Determine all c.p.'s in terms of…

A:

Q: - Verify whether the following ODE is exact and find its general solution. (2xy - sec²x) dx + (x² +…

A:

Q: Q2) Is the ODE separable or non dy x² + 3y2 2ху

A:

Q: Show that the following ODE is homogeneous then solve it. 2xyy' = x² + y?

A:

Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

Q: Q3) for f(t) = sec-(6t- 1) and g(t) = tan (6t - 1) show that s'() = g'(t). %3D

A:

Q: Use Euler method to approximate the value of y(0.2), given               ay' - by = ce^(kx) + mx  ,…

A:

Q: Prb $2 x sinx dx メt)

A: We have to Solve given Improper Integral using Residue Theorem as Follows :

Q: Given the multiple variable function f(x,y,z)= Ax*e - Bz² co{x²y* )+ Cx*y*z², where 1. the…

A: Answer

Q: (c) = y² %3D dr dy (d) y = sin x %3D

A:

Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: (b) Determine the by using the Chain rule with the following information: z = cos (x"y^) – sin (z +…

A:

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

A:

Q: y'(t) = y –+r, 1<t<2, y(1) = 2, h= 0.5.

A: Given: y'(t) =y-y2t+t3   where 1&lt;t&lt;2and the initial condition y(1)=2  with h=0.5The iteration…

Q: Find the general solution to the following ODE: dy dr - tan(r)y sec (r)

A: When a first-order differential equation is expressed in the form  dydx+Pxy=Qx, the equation is…

Q: To solve the following ODE with Euler Method and Richardson Extrapolation To find y(0.2) which h are…

A: Given that, the initial value problem                                               y'(t)=tet-y(t)…

Q: Is this correct?

A:

Q: The ODE dy (z+y+5) is separable. %3D dx Select one: O True CO False

A:

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.