Let y, = e*, y2 = xe* be two independent solutions of y" - 2y' + y = 0 ,x > 0 then the particular solution for the ex non homogeneous equation y" – 2y' +y = is 1+x2 Y(x) = %3D A. -; e* In (1 + x²) + xe* tan x B. - In (1+ x²) + tan x C. ex + xe* D. Ce* + C2xe*

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

Q: 7. Given y =x*in*, calculate y'. sinx sinx A) y'=xin* (sin.x Inx + cos x Inx) C) y'=x*inx + cos x…

A: For the solution of the problem follow the next step.

Q: 5) y"-y'-2y=x+cosx

A:

Q: What is the general solution of (1 + a2) y' = x*y %3D Oy"-3ay + 1 = C O ay - 3ry + 3y% tan-1 æ + 1 =…

A:

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: tan²xdx = sin³ydy when x = 2, y = 3

A:

Q: Convert 60013g to decimal. Show your work.

A: See the detailed solution below.

Q: i) tanzy dy sin3xdx

A: As we know that  (i)  tan2y=sec2y-1(ii) ∫sec2ydy=tany+C(iii) sin3x=3sinx-sin3x4(iv)…

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: Let u and uz be two solutions of the nonhomogeneous equation Ly] = y" + +y= sin(t). Then y = u - uz…

A: There is a theorem that which I am stating below:

Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

A:

Q: ах ) x' + 4x/y 5 y² = 3 ) Vxy +1 = y ) 3xy = (x' + y' ) ) x' +x.tan¯' y = y ) sin¯'(xy) = cos"' (x –…

A: Simple differentiation

Q: y= (1+x?)tan x- x? y' = 1 + xtan1-2x y' = 1 + xtan -2x y' = 1 + 2xtan 1-2x y' 1 + 2xtan -2x y'…

A: In this question we are required to calculate the derivative of the function.

Q: Find the solution of ordinary differentral equation X+2xy'-2y=L4xlox -5cos(Inx)

A:

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: y" + 4y' + 3y = sin (e*) %3D

A: follow next step

Q: The general solution of y''+4y'= 0 is ° y = C, + C,x+ C,e* ° y = C,e* + C,e²* + C;e2* -4x y = C,e* +…

A:

Q: An ant population grows at a daily rate of 3/10 times the current population. It is known that a…

A: Given, The number of ants die in each day (c)=36 The initial number of ants(P) =400 Let P be the…

Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

A: We will solve the problem

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: 2) (3x²y+ 4e)dx + (x³ + 4xe + 2y)dy

A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: tan(=2 ») =x+y. 5. tan Determine y'.

A:

Q: dv +w + v = 5 In solving differen tial equation system dx v(x) =? dw dv 9v = 10e*, dx dx A) v(x) =…

A:

Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

A:

Q: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

A:

Q: xt' + (t")3 = Và +5 x (3y')² ex² - y² = = (4x²y³ + y)²¹ y" 4 (cos x)² - y"

A: The given  differenrtial equation is xt'+t''3=x+54 Calculate the order of given differential…

Q: -(v/y)- o None of the above () ferentia uation y"+y' = 1? What is the general solution of the dif-…

A: given differential equation :-             y''' + y' = 1

Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

A:

Q: 2) (y+1)dx+(4x- y)dy =0

A: According to our guidelines, we can answer only the first problem or three subparts of a problem,…

Q: (D-9)y 3e" +x-sin 4x. 3 1 A. y C,e*+C,e* +e* +÷x- sin 4x 25 -3x 8 3 1 B. y Ce* +C,e-* +e* -x- sin 4x…

A:

Q: Solution of 2 y" = 1+y'² is

A: The given differential equation is y''=1+y'2 ......................................... (1)

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.