The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos 7x + c3 sin 7x) -7x O cie + (c2 cos 7x + C3 sin 7x) cjez + (c2 cos 7x+ c3 sin 7x) cielz + (c2 cos 7x – c3 sin 7x)

Q: The complementary function(C.F.) of the differential equation(D – 7)²(D+3)y = 7x is_ O (c1 + C2x)e=…

A: Differential equation and complementary function

Q: .D dy + x?y = sin(x) dx

A:

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: The complementary function(C.F.) of the differential equation(D-6)ʻ(D+4)y=6x is O (c1 + c2r)e + c3e…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: тен Solve the following differential equations Using D-Operator SITT 804 1.(D² - 2D-8)y = 6Cash 4x…

A: 1) The given differential equation is: D2-2D-8y=6cosh 4x The corresponding auxiliary equation is:…

Q: Show that (a) 8(at) =8(t), (b) 6(t) = 8(-t), %3D %3D la|

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: The complementary function(C.F.) of the differential equation(D - 5)y= cos 5æ is_ O (ci + c2a –…

A: Given that  (D-5)^3y=cos5x  To find the complementary function

Q: Solve the differential equatons (7x-ty +16) dy + (2x-5y+12) dx=o when x-3, y= 2

A:

Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

A:

Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: Write the smallest differential operator that annihilates the given 3x +x²e + sin(5x) e3 sin…

A:

Q: me complementary function(C.F.) of the di O (c1 + c2x + czæ²)e4z P (c1 + c2¤ – czæ²)et= - O (c1 +…

A:

Q: Find all values of a for which the equation : 10х — 2л2 — а - cos (2x + a) = x² – 8x – C cos 3 has a…

A: Given equation is  cos10x-2x2-a3-cos2x+a=x2-8x-a               (i) First, let us solve the following…

Q: Solve 4x+ 4x+6y +5 dy dx 3y+2x+4

A:

Q: -x2 Solve the differential equation xsec 2ydx + e by separation of variables. dy=0

A:

Q: 2. Solve - (D³ – D² − 6D)y = 12x − 2 + 5e³x – 18 sin(3x)

A:

Q: Which one is non linear differential equation O a. d³y +3x Y - 10y = x dy dx3 dx O b. dy + 8xy = 2x…

A: Differential equations are given, we have to find it is linear or non-linear

Q: The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots.…

A:

Q: The complementary function(C.F.) of the differential equation (D² + 6D + 18) y = is

A: Given: D2+6D+18y=x

Q: Consider the initial value problem (2xy² + cos x cosy) dx + (2x2y- sinx siny) dy = 0 and y(0) = 1…

A:

Q: which of the following differential equations can be solved using simple substituton? A. siny…

A: We have to find

Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A:

Q: The complementary function(C.F.) of the differential equation (D – 7)²(D + 5)y = 7x is O (c1 +…

A:

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: 2X 3- e 2X dy + 2 (Ye - x) dx =o dy + dx + Cosxy = tanx Sinx

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.