y" - 7y' – 6y = 3x² – 5x + 2 differantial equation is given. | 20 - the particular solution of this ODE; y=Ax² + Bx +C → A = ? O A) 2 B) 3 C) -5/3 D) -1/3 E) -1/2

Q: 3, Find the poner sertes solution in poners of (x-1) of *最+y=o; 0 2 +2y=0j つ4 4(メー)-4(メー)れ +…

A: Given that xy''+y'+2y=0 Take y=c0+c1(x-1)+c2(x-1)2+c3(x-1)3+c4(x-1)4+c5(x-1)5+.. Take the derivative…

Q: he general solution of the linear system X' = AX is given. 4 cos(4t) sin(4t) ) -4 sin(4t) +C, A =…

A: Given that , The general solution to the linear system X'=AX is given , A=-1-161-1 And ,…

Q: Q: Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z = 1 x- y+ 5z = -2 2x + y = 3

A: The given system of equation is  3x + 2y -z =1 x - y +5z =-2 2x +y =3

Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

Q: Q14- Solve the equations to find x, y, z by Gaussian elimination : 3 x+z = 4 2 -3 x+3y - 2 5 X - 5 =…

A: Given: The given system of equation is,

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: y = ", ‚ y(xo) = Yo

A:

Q: (2) Find the value of m so that y = emz is a solution for z'y"-y = 0.

A: Given that the differential equation x2y" - y = 0 has a solution of y = emx To find out the  value…

Q: Consider the DE У" - У" — бу %3D0 = e-2x and A) Verify that yı = 5, y2 y3 = ex are solutions of the…

A:

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

A:

Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

A:

Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

A:

Q: he auxiliary (charasteristic) equation of the DE x²y" + xy' – y = 0 is m? - 2m +1=0 m2 - 1 = 0 m2 +…

A: Givenx2yιι +xyι -y=0

Q: Q Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z 1 x- y+5z = -2 2x + y = 3

A:

Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

A:

Q: Show that y1(t) = et and y2(t) = e−3t form a fundamental set of solutions for y'' +2y' −3y = 0, then…

A: If y1(t)  and y2(t) are two solutions to the differential equation…

Q: Let x, y be the unique solution of x' = y y' = 0, y(0) = 1. = -x x (0) Show that x, y verify x2 + y?…

A: Given x' = y                   (1)y' = -x                (2)x(0) = 0                    (3)y(0) = 1…

Q: When does an nth order, homogeneous, Cauchy-Euler equation anty(n) + an-1tn-ly(n-1) + +aity' + aoy =…

A: Given: nth order To find: Cauchy-Euler equation

Q: (1) こ Wy2,y2)= 12 enx (2) 9/2 X 9) Y=(x)=e

A: It is given that the differential equation y"+3y'+y=0. Wronskian W(y1,y2)=12enx            ......…

Q: Assuming that a DE has a general solution a+y= 3r +C, what is the particular solution at given the…

A: The given differential equation has a general solution is x+y=3x+C. Calculate the particular…

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

A:

Q: Find the solution of xy" + 5xy +(4 – Ix)y = 0, x > 0 of the form where co = 1. Enter n= 1,2,3, ...

A: Let the solution of the above differential equation is given as: y=xr∑n=0∞cnxny=∑n=0∞cnxr+nThe…

Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

A:

Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

A:

Q: it as a Bernoulm cquaion in the uependeht varlavic A. 0. 2x'y = y(y? + 3x). Solve by two methods.…

A:

Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

A:

Q: 2 Find the solution. ху'+ ху %3D 1-у, у(1) %3D 0 A y = x-'(1 – el-') B x = y-'(1 + el-) В © 2y =…

A: Solution of the differential equation

Q: 4. Solve the equation T2T satisfying the conditions: at ax (i) T=0 when x= 0 and 1 for all t 2x,…

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

Q: 2. у" — у' — х %3D 0

A: To solve the given differential equation.

Q: (b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

A:

Q: 2. Find te gunural soiUtion of 2

A:

Q: An Euler-Cauchy equation is given as x*y" +1.5xy – 0.5y=0, x(1)=5, 19 (9). 3 Solve the equation by…

A: Here, we have given that the Euler-Cauchy equation x2y''+1.5xy'-0.5y=0 and the initial conditions…

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

A:

Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

A: The solution of differential equation y’’+6y=0 is

Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

A:

Q: 8. Obtain the particular Solution by satisfying the conditions indicated. y' = x exp (y - x²); when…

A:

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

A:

Q: Use the method of variation of parameters to find a particular solution of the DE (3x – 1)y" – 9xy'…

A:

Q: Find two values of n such that y = enI is a solution of y" + y' – 72y = 0

A: Given differential equation,  y'' + y' -72y = 0 To find the solution of above equation in form of…

Q: 2x2yn+3xy'-y=0 , x>0  in the equation given as: y1(x)=x1/2 ve y2(x)=x-1 verify that there are…

A:

Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

A:

Q: = 1 on the domain a² < x² + y² < b², Question 3. Solve the equation uxx + Uy with u vanishing on…

A: Consider the given equation: on the domain with u vanishing on both the boundaries

Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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.