The complementary function(C.F.) of the differential equation (D + 6D+ 18)y-zis O (e +ez)e * O "(e cos 3z - o sin 3z) O (e cos 3z + o sin 3z) O e"(e cos 3z + eg sin 32)

Q: sin (t) -dt 3 (4+ cos (t))?

A:

Q: Cos x sin (sinx) dx

A:

Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: 05 y' + (cot x) y 3 sin x cosx

A: We have to solve the given differential equation.

Q: (sin°(3x) + sin²(3x)) cos(3x) dx

A: We have to find the indefinite integral.

Q: Solve the equation (x+2) Siny dx + X cosydy=1 собуду=0

A:

Q: Solve dy dx cos x = cos x cst ² y

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

A:

Q: Solve dy/dx=sin(x+y)+cos(x+y)

A:

Q: (3x + 1)'3 dx

A:

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: 3. a) Define Integrating Factor and Exact Differential Equation. b) Solve: (x2 + xy-y² )dx+ x² - 2xy…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve: y" + 2y' + 2y = 2 sin(x) +3 cos(2x)

A:

Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

Q: Verify that (e* sin y-2ysin x)+(e* cos y+2 cos x)y' 0is exact. Then solve it and leave the answer in…

A:

Q: Solve the DE (D-1)y= 3 sinx+ 22 - 2x°2

A:

Q: (cos y + y cos x) dx - (x siny - sinx) dy = 0

A:

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: Use the method of undetermined coefficients to solve y" – 2y' + y = 5 cos(2x) + 10 sin(2x)

A: Solve the differential equation y"-2y'+y=5cos2x+10sin2x using the undetermined coefficients .

Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: What is the general solution to the differential equation A B C y = arcsin (esin 2) + C y =…

A: The given differential equation is:dydx=cos(x) esin xcos(y)

Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

A:

Q: Solve the ODE with differentials operator (D²+4)y= cos(2x) + cos (4x)

A: Linear ordinary differential equation

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.