3- y = 2 + cos²(x? Q\(20 M) Classify the following D.E to: order, degree, homogeneous, and linear: d'y =y - 4 1- x dr 2- (2x – y + 4) + (xy – 2y + 5) = 0 3- y=+ cos*C) dx 4-y"-xy'=2sin.xy 5- y"+y'+6y =3

Q: find dy/dx

A:

Q: If (x, y) moves from (-2, –1) towards (1, 5) for a distance 0.02, then which of the following is…

A: fx,y=exyPoints from−2,−1 towards 1,5 for a distance 0.02

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

A:

Q: dy using implicit differentiation: 4x°y² – /æ +3y = 57 Find dx %3D O dy -20z'y² + }a¯1/2 8r°y+ 3 dz

A: Given,            4x5y2 -x + 3y =57

Q: Problem 4. For the matrix A find all eigenvalues and all eigenvectors. Determine an algebraic and…

A: Given A=4-234 We will find all the eigenvalues and eigenvectors. Definition: Let A be an n×n matrix.…

Q: If w= y(x- mz)i + yz*j + In XZ -1 k and f-w cos (xy-x) x* + m y find at point (0,2.-m): (1) the…

A: Given - If w = yx - mzi + yz2j + lnxz - 1x2 + mk and f = w ·cos-1xy - x2yj To find - At point ( 0,…

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

A:

Q: Identify the type, order, degree, DV, IV and name of the DE. (y'")3+5(y")2-2y' - 5y=0

A:

Q: dx Xex+10, Complete the Square.

A: Given,          ∫1x2+6x+10dx

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: dy Find for the given implicit functions: dx а) у? - ху%3D2 b) 2.x sin (xy)– x = 0 c) (xe')" + y = 3

A:

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

A:

Q: Find the derivative of y. 30) y = In (sinh 5x) D . sinh 5x A) coth 5x B) 5 csch 5x C) 5 coth 5x

A: We can answer the question as below.

Q: Find df and dxo f , and write (dxo f )(X – Xo). (a) f(x, y) = x³ + 4xy² + 2xy sin x, Xo = (0, –2)…

A:

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: 2. Complete each of the following. a) Let [x] € Z/nZ. What is the additive inverse of [x]? b) Show…

A:

Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: g) The integral S tan(vx) dx x cos2 (Vx)

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

A:

Q: r1/V1-x 70. (2y + 1) dy dx |-1/Vī=x

A: Consider the provided integral ∫-11 ∫-11-x211-x2 2y+1dydx. Solve the provided integral. ∫-11…

Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

A:

Q: dx 7. = cosx cos² t dt

A: 7). To solve the differential equation: dxdt=cosx cos2t Solution: Re-arranging the given…

Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

A:

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

A:

Q: f(x, y) = xsin²y + y² cosx, Find fxy a. sin² y - y² cosx b. 2xsinycosy-2ysinxcosy c. 2sinycosy -…

A: We need to find fxy.

Q: dy – y (xy' -1) .3 2.) dx

A:

Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

A:

Q: 1. dly dx 64XY

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: x. y'"' – y" = x². sin 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.