Consider the following differential equation y" + 4y/ + 5y = 0 Select the correct solution set to this differential equation Select one: O a. S = {a · e¯2= . cos(2x) + b · e-2= . sin(2x)|a, b € R} O b. S = {a · e² . cos(-4x) +b · e²= . sin(-4x)|a, b € R} O c.S = {a · e2= +b• e²=\a, b € R} O d.0 O e. S = {a · er. cos(-4x) + b · eir . sin(-4x)|a, b E R} O f. S = {a · e¯4z . cos(2x) + b -e¯1z . sin(2x)|a, b E R} O g. S = {a · e · cos (2x) + b · e . sin(2x)|a, b E R} O h. i

Q: x*cos(y/x)*dy/dx = y*cos(y/x)-x   find solution of that differantial equation.

A: Let us consider the differential equation of the form dydx=fyx  then to solve the differential…

Q: I.x''-9x=cos(t) II. x''+9x=cos2(t) III. x''+4x=sin(2t)   Solve equation-(I) using the method of…

A: We are entitled to solve only one question at a time. Given - x'' - 9x = cost To find - Solve…

Q: .v" + y = cos x ; when x = 0, y = 0, y' = 1

A:

Q: solve et (l-t)? with y coJ=2 and y'Co)=6

A: We have to solve

Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

Q: sinh e/2 dx is equal to e/2 2 cosh e 7/2 + C 2 cosh e"/2 + C O - (sinh e /2) + C 1 O -2 cosh e I/2 +…

A:

Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: Find the general solution of the equation: y' -2y = 2 sin(3t).

A:

Q: y" - y' - y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: Given :y''-y'-y=cos5t-sin5ty(0)=2 and y'(0)=5

Q: cos(sin−1(x) − tan−1(y))

A: Important points:  cos(A + B) = cos A. cos B - sin A. sin B sin(sin-1x) = xcos(cos-1x) =…

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: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

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: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

A:

Q: dx

A:

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: Solve the equation y' = csc(x) - y cot(x).

A:

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: Chosse the correct answer. A particular solution of x'' + x' - 2x = 2sin2t is given by: Xp(t) =…

A: Given non-homogeneous differential equation x''+x'-2x=2sin2t    ...(1). We have to find the…

Q: y(5)_y(3) = e²+2x²-5 y(4) + 5y" + 4y = sinx + cos2x

A: Given: The equations are y5-y3=e2+2x2-5 and y4+5y''+4y=sin x+ cos 2x. The objective is to find the…

Q: 2 sin(2x) - 3 cos(x) dx

A:

Q: 2) Find the general solution of the equation 1 y""+y' = (sinx)3

A: The  given equation  is  The auxiliary  equation is  given by…

Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Q: (4) sin 0 de 프2

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Given the differential equation: D´(sin x- cos x+ 3e* +x²) What is the fourth derivative? a - sin…

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.