Choose the second order linear non-homogeneous differential equation(s). d²y = 3a dy i. dx? dx d's ds + ks = 0 dt ii. %3D dt? dx +y=0 dt iii. iv. -4y"+2y = 2x O . iii and iv O b. ii, iii and iv O c. i and ii O d. iv only

Q: 4. For each of the following systems of differential equations, find the general solution and then…

A: Do mention that , as per our guidelines we are supposed to answer only? 3 sub- parts ( if there are…

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given solution to a linear non-homogenous differential equation is    yt=c1et+c2e2t-3tet+cost-e-t2…

Q: Obtain the differential equation of the given family of curve: y^2=x^3/(c-x) O A. 2x^3 y^'-3x^2…

A: Explanation of the answer is as follows

Q: What is the standard form of this linear differential equation in one variable, y + 1)dx + (4x – y)…

A:

Q: If one of the solutions of a third-order differential equation is x²e", determine the differential…

A:

Q: Consider the differential equation (xy + 3x - y – 3) dx (xy – 2x +4y - 8) dy. By separation of…

A: Please refer the attached image for complete solution.

Q: Discretize the differential equation y" – 2y' + 4ty = 2t, y(-1) = -2, y(0) : -2 with step-size h %3D…

A:

Q: of two linear first-order ordinary differential equations: y1 = 2Y1 – 2y2, Y2 = Y1 – phase portrait…

A:

Q: 5- dx3 d'y + 64 d'y dy + 137 dx dx2 30y = 0 A. y = ce0.2x + Cze-3* + C3e-10x + cze-3x -10х B. y =…

A: Given that: 5d3ydx3+64d2ydx2+137dydx-30y=0

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A:

Q: Which of the following is the transformed form of the 2y = x(y')³ – (y')² +1 differential equation…

A: We have 2y=xy'3-y'2+1 Now , differentiate both sides with respect to x:…

Q: To reduce the differential equation with linear coefficients (X +2y-4)dx – (2x+ y- 5)dy=D0 to a DE…

A:

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is…

A: We are given the solution as : y(t)=c1et+c2e2t-3tet+cos t-e-t2 ---(1)…

Q: Obtain the general solution of the given homogeneous differential equations.

A:

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: We have to find the homogeneous linear differential equation with constant coefficients whose…

Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

A:

Q: determine two linearly independent solutions to the given differential equation on (0,∞). Q.…

A:

Q: Determine the appropriate form for yp on the differential equation y"=9x^2 + 2x -1 a. y=Ax^4…

A: given the differential equation :

Q: Discretize the differential equation y" – y' + 4ty = 8(t – ), y'(1) = 0, y'(4) = 0 with step-size h…

A: Given ODE is : y"-y'+4ty=δt-52 , y'1=0 ,y'4=0  Since, we have the boundary condition of third kind ,…

Q: Consider the first order linear differential equation with constant coefficient and constant term,…

A: As per instructions we are allowed to answer only three subparts. Complementary solution : It is the…

Q: Convert the differential equation u'' - u' – 2u = e-5t into a system of first order equations by…

A: Given: u''-u'-2u=e-5t

Q: Consider the ordinary differential equation y" + 4y' – 4y² - -2t. y(t) and y2 y'(t). Write down an…

A:

Q: Which of the following systems is equivalent to the differential equation y" + 9y" = cos(x) – y? 9uz…

A:

Q: d³y +3(1- a)z² d´y dy + (3a? – 3a +1)z- - a'y = 0 dz dz

A: We have to find the value of the variable a.

Q: Determine the differential equation of the family of lines passing through (h, k). A. (y- k) dx -…

A:

Q: 4. For each of the following systems of differential equations, find the general solution and then…

A: please see the next step for solution

Q: To reduce the differential equation with linear coefficients (x+2y- 4)dx– (2x+ y- 5)dy= 0 to a DE…

A: We have to convert given differential equation into dydx=f(x,y)  form and then find proper…

Q: Find the solution of the nonhomogeneous differential equation initial value prob- lem 3. dy dr3 y(0)…

A:

Q: roblem, y = 1/(1 + c,e*) is a one-parameter family of solutions of the first-order DE y' = st-order…

A:

Q: What is the auxiliary equation associated with the second order linear differential equation d^2x…

A:

Q: Consider the non-linear differential equation * =- x+ y – 1 ў 3 2х + х3. Draw the nullclines and a…

A: Regression Analysis:              Regression analysis helps to estimate the changes when…

Q: Form the differential equation for the function 2x-y-asin(2x-b) O a. y"+y=x O b. y" +8y = 4x O…

A: Given, 2x-y=asin(2x-b)

Q: 1. Convert the second-order differential equation d'y + 2y = 0 dt2 into a first-order system in…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: To reduce the differential equation with linear coefficients (X+2y-4)dx - (2x+y-5)dy=D0 to a DE with…

A: We are going to solve

Q: Here is a homogeneous second-order linear differential equation, two functions y, and y2, and a pair…

A:

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

A: We need to find auxiliary equation.

Q: Convert the differential equation u'' – 3u' + u = et into a system of first order equations by…

A: Given differential equation is u''−3u'+u=e3t.....1 We have to convert the given differential…

Q: 2. Sketch the phase line and identify the equilibrium points for the differential equation dy - 3y…

A:

Q: Convert the equation d°y dy -3 x y 0 dx3 -3. and initial conditions y(0)= 1.11983, y'(0)=0.83697 and…

A: Introduction: A higher order linear differential equation can be converted into a system of first…

Q: Find the general solution of the second order linear differential equationd^2y /dx^2 −dy/ dx − 12y =…

A:

Q: Find a second order linear differential equation with constant coefficients for which the following…

A:

Q: The solution of the differential equation by variable separable method dy (1+y²) (3z²+6) dz 1³ +62…

A: Given :  The differential equation is ;   dydx = 6 1+y23x2+6x3+6x To find : The solution of the…

Q: The formation of the partial differential equation by eliminating arbitrary constants a, b from the…

A:

Q: order differential equation: a. y’ = 3y + e2x           b. y’ = ___t2___           y( 1 + t3 )

A:

Q: The reduced form of the given Bernoulli's dy dx + 3xy = 4xy³ to differential equation the Linear…

A:

Q: Obtain the differential equation belovw. y = Ce* + Cze-3x O y-3y +2y = 0 O y- 3y-2y 0 O y" +2y +3y =…

A: y=C1ex+C2e-3x

Q: Find a second order linear differential equation with constant coefficients for which the following…

A:

Q: btain the differential equation of the given family of curve: y^2=x^3/(c-x) O A. x^3 y^'+x^2 y+y^3=0…

A: