y = C, cos 3x - C sin(-3x)

Q: Solve the differential equation: sin(2x)cos(y) − sin(y)sin2(x)dy/dx = 0

A:

Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: sinx dy = 0 y cos xdx + 1+

A:

Q: (3ху2 — у?)dx + (2х?у - 2у)dy - 0

A:

Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

A:

Q: Find the solution of the differential equation y"+y' = sin x %3D

A:

Q: Solve the differential equation: sin y (x+siny)dx+2x2cosydy=0

A:

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''+y'-3y=4sin2x

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Solve the differential equation by variation of parameteres: y'' + y = sec(x) + tan(x)

A:

Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

A:

Q: Solve the given differential equation by undetermined coefficients. у" - бу" %3D 2 - cos(x) y(x) :

A:

Q: y = Ae* + Be-*

A:

Q: Find the general solution of the differential equation y′ = tan3 3x sec 3x

A: Given: y' = tan3(3x)sec(3x) =>dy/dx = tan3(3x)sec(3x) =>dy = tan3(3x)sec(3x) dx

Q: Find the general solution of the differential equation, (5e-3 sin (3x)) dx + (5xe-y + 2 cos(3x)) dy…

A:

Q: Determine the solution to the differential equation given by: y''-2y'+y=sin x

A:

Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: y' + (2 tan x)y = - cos'x

A:

Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

A:

Q: Use separation of variables to find the general solution of the differential equation. 6 cos(tx) xp

A:

Q: 4. xy = x cos( y/x)+y

A:

Q: Find the general solution of the differential equation y′ = √(tan x) sec4 x

A: The function is y'=tan xsec4x. To find the general solution, integrate both sides of the equation.…

Q: xcosydy + sin2ydy – dx = 0

A: First arrange it in the bernouilli equation then find its integrating factor. Then  use the formula…

Q: Solve the differential equation by variation of parameters. y" + y = sin2(x) y(x) =

A: The given differential equation is: y''+y=sin2x

Q: Form the differential equation for the function x+2y=a sin3x-bcos3x

A:

Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: dy cos(x). + y sin(x) = sin²(x) cos(x) y³ dx

A:

Q: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: Consider the differential equation curve if it passes through (1,-1). dy 2y dx x = 0. Find the…

A:

Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos ex y(x) =

A: Given differential equation is y''+3y'+2y=cos ex The auxiliary equation is…

Q: Find the Differential equation by eliminating the arbitrary constant  Sin-1 x + sin-1 y = C

A: sin-1x+sin-1y=C

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: Give the general solution of the differential equation y'-y = sinx + cos2x +e-x

A:

Q: Solve the 2nd order linear differential equation y" – y' = 5e* – sin2x %3D

A: The auxiallary equation for the given differential equation is given by

Q: general

A: Please refer to the image below

Q: y = 2 -[(1+y(t))sin tdt.

A:

Q: Solve the differential equation by variation of parameters. y" + y = sin(x) y(x) = %3!

A:

Q: (メyーx+24 -2) dx- (x+ 4x) 0

A:

Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

Q: Solve the differential equation by variation of parameters. y"+ y = sin(x) %3D x cos(x) y(x) =…

A:

Q: Find the differential equations having as solution of y = x sin(xtc) .

A: We find the differential equations having as solution of y = x sin(xtc) .

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) =

A:

Q: Find the general solution of the differential equation: y′=(1+y)secx+tanx

A:

Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

A:

Q: Write the general form of Cauchy-Euler differential Equation. Solve the follow- ing differential…

A: General form of Cauchy-Euler Differential Equation. The differential equation…

Q: Find the homogeneous linear differential equation whose solution is y=-e^(3x/2)-4x sin⁡2x.

A:

Q: dy_ y²sec² (-) tan (-) dx x2

A:

Q: Solve the differential equation using the method of undetermined coefficients. y" - 4y' = sin(3x)

A: Given differential equation is

Q: Find the solution of differential equation 4º+y = sin dx2

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.