The general solution for the DE - 2y +y=xe",x>0, is given by O d. y= Ce* + c2xe* – xe¯\Inx. O e. None of these O C.y= ce* + czxe* + x ¯le%Inx. O b. y= Ce*+ c2xe* + xe¯\inx. O a. y= Ce*+ czxe* + xe*Inx.

Q: 5. Find the homogeneous differential equation whose general solution is y = 3 cos x - e³x/2 - 4x sin…

A: Note:-“Since you have posted multiple questions, we will provide the solution only to the first…

Q: Which of the following expressions is equal to (A) B (С) (D) 2 1.² 2 S. ² 1.² X 2 X 5 X 3 - 3 4 3…

A: Solution: Write the fraction using partial fraction decomposition.

Q: 2. Sキ 1 dx 5+x2

A:

Q: 2. x = u² + 1, y = 4u² – 4u

A:

Q: dz 4. Compute where

A: We can solve the problem by residue method

Q: 2. Find the divections..in.w.hic . fCx,y) = X- a.. Increases.ms..rapidly.at. paint.C1). b. Decrenses…

A: Solution: The given function is fx,y=x22+y22    ......(1)

Q: The number of units in z3,[x] is 30

A: We know that, any ring given as ℤpx  will have  (p - 1) units

Q: Kira recelved a S80 gift card for a coffee store. She used it in buying some coffee that cost $7.91…

A: To find the pounds of coffee she bought

Q: 6. Find the quotient +(-).

A:

Q: If fix.y)-y", find fa

A: Here we have to find the second partial derivative of the given function.

Q: (х + 3)dx бх — х2

A: ∫ (x+3)dx/(6x-x2) ∫ (x+3)dx/x(6-x)  -∫ (3/2(x-6) - 1/2x) dx  -3/2∫ dx/x-6 + 1/2∫dx/x {ln(x) -…

Q: A Presentatio xA Presentatic x *Dashboar Xx 9 Science 8: S x O Schoology x Unit 4: Do x O (15) Me X…

A: Solution:- it is a linear function.

Q: Solveit. 2 3X

A:

Q: < Use exact numbers. y = ←++ x+ -9-8-7-6-5-4-3-2 9 8 7 23456 6- 5- 4+ 3 2- 1- ST -4 -3- -5- Y -6- -7…

A: from given graph two points on line are (-2,0)  and (4,1)standard form of line is y=mx+cwhere m is…

Q: 8- Evaluate S² -2-y Jy x+y dxdy

A:

Q: (x– 3) - ? = ? 5. For x2 # 9, x' -9

A: Given Data: Expression: x-32x2-9 Condition: x2≠9

Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: why discontinuous  if lhl and rhl are same zero

A:

Q: 2. Show that 1 2 = (1 - )( - )(? y)

A:

Q: 9. If 4x(y+2) ソー3 O J6 4x(y+2) – 2x, y # 3 or -2, and x #0,2= ソ-3 y+2 A) B) C) 2 1/8112 28

A:

Q: ) g)=マーSr -2-Sr g(カー

A: solution

Q: If xly, then show that ||x+ y|| = ||x- y|!.

A:

Q: Vin3 Vin3 dx dy

A:

Q: Acere late ttesigned so that the first two characters are fletters and the last four characters are…

A: In the license plate first two characters are letters and last 4 characters are digits from 0-9.…

Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: 6. b = 1+35 + 35, 5 +3 A, 5+3-1= B a. If (25)* = (125) then determine y: x b. Show that, b³-3b-6b-4=…

A: Note:- For this problem, you don't mention about "b" in part (b), Will i have to use values of b and…

Q: 10.10) What is the least common denominator of (1 Point) 3 and 1 ? 3x3 6r2 9x O A.9x B. 18x O C.27x…

A:

Q: 6. Suppose A = (3, -2, 4), B = (-5, 7, 2) and C = (4, 6, -1), find A × B.A+B-C.

A:

Q: (:) If rank of A is r and if B : , then the rank of B is: C ar O b. 2r Od.0

A: Given, the rank of matrix A is r. Then we have to find the rank of the matrix B=AA.

Q: Solve for x. 6. 6x-1 *+3

A:

Q: (2 + In x)³ -dp-

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.