3 ± 5i If the roots of the auxiliary equation of a higher-order homogeneous differential equation are m = what is y? A y =- (C, cos (5x) + c, sin (5x)] 5x 5х y = e*½ + C, cos sin 2 5x 5x + С, sin (c) y=2e3x cos /2 [c, cos (5x) + c, sin y = e

Q: Q2:- Check that the indicated functions are solutions to the given differential equation :- 1) y" +…

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

Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K…

A:

Q: Find the value of a and b for which the given differential equation is exact: *siny + (a - 3)ysinx)…

A: Equation is exact for the values a= 5 and b= -1 Therefore option C is correct

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 16) cos(y) dy = 0 is given by In(x? + 16) +…

A:

Q: If y1 = cos 3x and 2 = sin 3x are two solutions of a second linear differential equation. Then the…

A: B. 3

Q: In this problem, y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y' +…

A:

Q: The non-homogeneous differential equation P(D)y = cos(2x ) has associated the characteristic…

A: I am attaching image so that you understand each and every step.

Q: 4. Find the differential equation of the family circles entered at (h, k) passing through the origin…

A:

Q: 4. Find the particular solution of the differential equation (10x + 6x siny)dx + Vx?…

A:

Q: The general solution of the differential equation d?y + 6y = sin 4x is dx 2 sin 4x O y = c¡ cos /6x…

A: The given differential equation is d2ydx2+6y=sin 4x. Consider the homogeneous part of the given…

Q: 2. The general solution to the differential equation below is: * - k²x = 0 , x= sin(ky) %3D dy? Not…

A: Ggg

Q: y" + y = 10 cos t e-t + 2 t?

A: Consider the given differential equation:

Q: alfae 102 K/s & ll45 | 4:33 PM The solution of the following separable differential equation y' =…

A: To find  The solution to the given separable differential equation

Q: 4) Solve the given differential equation by using undetermined coefficient annihilato operator…

A: To find the annihilating operator of terms in RHS of the given non homogeneous differential…

Q: Given: (1+ 2ytan x)dx - dy - 0, determine the solution to the differential equation. O a. 2y cosx-…

A:

Q: Solve the exact differential equation (In y -y sin x-6ex)dx +( + cos x + 5 sec y tan y -6y)dy = C y…

A:

Q: Given the second order non-homogeneous linear differential equation y" +2y-3y 3 ex+4 cos x,…

A: Given differential equation is y''+2y-3y=3ex+4cosx We can write the equation as (D2+2D-3)y=3ex+4cosx…

Q: Consider the differential equation: 1. y"-y%D What is the general solution? y= [a + In(1 +te *)]e* +…

A:

Q: 1. Consider the 2nd order differential equation d²f 2 df + Af (=)=0 dz² z dz To solve the problem…

A: As per the question we are given a second order linear homogeneous differential equation. And we…

Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

A:

Q: The value of k so that the differential equation (6xy³ + cos y) dx+ (3kx? y? - x sin y) dy=0 is…

A:

Q: Which one is false? If the auxiliary equation of the homogeneous linear differential equation has…

A: Let us check which of the information given is false in the next step.

Q: For the differential equation x" + 4x = 0, find the solution to the IVP if the two-parameter family…

A:

Q: Consider the differential equation (10x*y4 +e-y + 3 sin(4x + 3y))y' + (6x²y³ + 4sin(4x + 3y) + 2) =…

A: Exact differential equations

Q: (b) Given the differential equation (DE) (y cos r- ka'y- 2r)dr+ (2y sin z- + In y)dy 0. %3D (ii)…

A:

Q: The solution of the separable differential equation – x²y² = x² is: dx None of the above…

A:

Q: 4. Solve for the general solution of the differential equation using homogenous equatiorn [x cos?…

A:

Q: Solve the differential equation -1 (x + 3)¯¹ cos (y)dx cos (y)dx O a. cos (y) In b. cos (y) In -…

A:

Q: Show that y a solution af y +2xy =0, Show that y = ka solution of y" - 3y' + 2y - 0. (12 sin(3x)…

A: We have to solve the first and second problem, we subtitute the value of y, y', y'' and y''' in the…

Q: In this problem, y = 1/(x² + c) is a one-parameter family of solutions of the first- order DE y +…

A: Given:- y(x)=1x2+c is one parameter family of solution of DE y'+2xy2=0Initial condition: y(3)=15To…

Q: Solve the exact differential equation (In y - y sin x-6e)dx+(÷- + cos x + 5 sec y tan y -6y)dy = 0 A…

A:

Q: 2. Find the particular solution of the differential equation (1 – cos(2t)). dt da a sin(2t) given…

A:

Q: Consider the differential equation y" – 2y'+ 37y = 0; e* cos(6x), e* sin(6x), (-o, ). Verify that…

A: y(x) = ex(C1cos6x +C2 Sin6x)

Q: 1. Consider the following first-order ordinary differential equation 2,2 2x²y cos x dy + (2xy² cos x…

A:

Q: For the differential equation y' + 4y = 0, a general solution is of the form y = C, sin 2x + C2 cos…

A: Given initial value  problem y"+4y=0    , y(0)=-2 , y'(0)=-10 y=c1 sin2x  +c2 cos2x

Q: Find the solution to the initial-value problem. y' = −8x tan(y), y(0) =  ? 2 y =

A:

Q: The solutions of the homogeneous(non-second handed) part of a differential equation with constant…

A:

Q: Q-2) [CLO1(PLO1)] Solve the given differential equation subject to the indicated initial condition a…

A: 2) Given differential equation is  α +11 + y2 + cosx - 2xydy - yy + sinxdx = 0,   y(0) = -1

Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

A:

Q: To solve the ordinary differential equation dy 4- + 5y? = sin x , y(0) = 5 %3D by Euler's Method,…

A:

Q: 3. Given the DE with the form y' + yP(x) = (y^n)Q(x), where n is any real number. If n = 1, the…

A: I have show that for , n=1 given differential equation becomes variable seperable differential…

Q: Solve the differential equation y' = e4Y sin(5x) and choose the correct answer from the following…

A: Given:- y'=e4y sin(5x)  To find:- General solution of given differential equation

Q: Solve the differential equation sin 2y dx - 3x-cos 2y dy = 0 by separation of variables. (A ex² _…

A:

Q: Consider the differential equation: y" + y = sec x,0 <x <n/2 What is the particular solution y.? Yp…

A:

Q: Consider the differential equation: y" – 10/ + 24y = 8e cos(2r) – 6e sin(2x). a. Find the general…

A: Given that y''-10y'+24y=8e4xcos2x-6e4xsin2x (a) Now take, y''-10y'+24y=0 Take m=ddx…

Q: To find a particular solution for the differential equation y"+4y = tan r with the variation of…

A:

Q: For the differential equation y" + 4y' + 13y = 0, a general solution is of the form y = e-2* (C1 sin…

A:

Q: 3. Show that the differential equation (cos z + 2y) dy + (r³ – y sin z) dr = 0 is an exact equation…

A: