Find the constants a, b, c, and d so that b + Dª + aD³ + D² + cD + 4d]y=0 has a solution of the form Ecos(2x) y= Ae¯X+ Bxe2x + Ce2x + De 2Xsinx cosx+ e2x

Q: Find the solution formula of u(x, y) for Uxx + Uyy = 0, uy(2,0)=0, u(x,b)=0, u(0, y) = 0, u(a, y) =…

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

Q: The general solution for the Euler DE x2 +2xv -2y%3D0,x>0, is given by O b.y= Gx=2+ C2X. O d. y=…

A: The general solution to the Euler DE  is , where, are the roots of the equation, .

Q: Find the particular solution of y" + 3y' + 2y = -9sin x + 23cos . ||

A:

Q: 7. For what values of k will the system 2z + ky + z = 0 (k - 1)r - y + 2z = 0 4z + y + 4z = 0 have…

A: Determinant be zero for non-trivial  solution

Q: Find the general solution of 6y''+y"- 15y'=0, 3x 5x A y=c,x+cze 2 +Cze 3x 5x B y=c,+c,e ? +c.« ¯ 2…

A:

Q: Find a particular solution of (15) y′′−3y′−4y=−8etcos(2t).

A:

Q: Solve the DE y'=(x+y+2)^2, y(0)=2 by setting u=x+y+2.

A:

Q: The solution of the IVP y = x2(1+y), y(0) =3 is O None of these. y= 4e 3 - 1. y3 xe + 3. .3 3. y36e…

A:

Q: Let u(x, t) be the solution of n. и = xt, -00 0, .2 ди (x, 0) = 0, –00 < x < ∞. u (х, 0) - %3| -…

A:

Q: 17. Find the general solution of * (4D + 4D3 - 3D² – 2D+ 1)y = 0 y = (Cr+Ca)et +(Ca + C)e y = (Cr +…

A:

Q: Show that if ad - bc ≠ 0, then the system ax + by = r cx + dy = s has a unique solution.

A:

Q: Show that r =1+i, x2 = 1- i is a solution of (3+ i)x1 + (1+ i)x2 = 4 + 4i

A: The solution is given as

Q: B. Prove that the given equation is a solution to the given DE: 1. = C,e3* + C2e²* + C3e* ; y"" –…

A:

Q: 7. Solve for x, y and z using Gauss-Jordan Elimination 2w + x – 3y – 3z = 4 x + 2y +z = -3 2w – x +…

A:

Q: 1. y" + 4y'+ 3y = 12 В. 12 А. 4 С. -4 D. 4x

A: Given y''+4y'+3y=12(D2+4D+3)Y=12Auxillary equation is m2+4m+3=0Upon solving, m=-1,-3CF,…

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: The general solution of xy" - xy' + (24x* – 24 y = 0, is .a - C,xY,(2 /6x) b O C,xJ,(2 6x) +…

A: We have to find the general solution of the differential equation…

Q: Prove that y = C,x² + C2x²lnx is a solution of the different equation x2y" – 3xy' + 4y = 0 and then…

A:

Q: Which of the following is the solution of ди +2- ди Ox 0 = a) u(x,y)= e"-2x b) u(x, y)= (2x + y)³ c)…

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: Which of the following equations is the DE whose solution correspond to y = C1sin3x + C2cos3x + 9x²…

A:

Q: Find the closed form solution of B(1) = 1, B (n) = B + 2n, n > 1,n E Z

A:

Q: Find the solution of the Euler-Cauchy equation x²y" + 0.6xy' + 16.04y = 0.

A:

Q: Let f(x,y) = C be the solution of the DE 2e3cos(vin(x)dx-3xsin(y)e3cos(in(x))-dy%3D0, where (x,y)…

A: We need to find value of C.

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: (a) Verify that yp, = 3e2* and y,, =x² + 3x are, respectively, particular solutions of y" – 6y' + 5y…

A: To verify the given statement and to find particular solutions by using the given statement.

Q: A) Verify that y = C1 + ©2x* is a solution of the DE: z²y" – 3ry' = 0. B) Find a solution to the…

A: We have to find the solution of given homogeneous differential equation with constant coefficient…

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

A:

Q: find the genral solution (D +2D,D, -2D, +2)u = 0

A: Given  Dx2+2DxDy-2Dy+2u=0   …………………(1) Consider the equation F(Dx,Dy)u=0 Here F(Dx,Dy) =…

Q: A solution to the DE ydx-xdy=0 is A B C D xy=C x = Cy none of these x=y=C

A:

Q: Let y(x) be the solution for the DE : y = (x + y – 1)² If y(0) = 1, then find y() %3D %3D 4 37 8- 7…

A:

Q: -** Find the solution set in c Z² + 2i(32i) = 3Z

A:

Q: The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x,…

A: Consider the given information. utt=uxx                 -∞&lt;x&lt;∞t&gt;0ux,0=2xutx,0=e-x D…

Q: Consider the following IVP: y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b Find the solution. A y(x) =…

A:

Q: Find the solution of the Euler-Cauchy equation x?y" + 0.6xy' + 16.04y = 0.

A:

Q: Given that 212-y? - 2r c is a one-parameter family of solutions of the DE dy = 2r - 1, dr %3D find…

A:

Q: A. If:Z = x + iy, Solve the following equation to find x and y: 4x+ y_ 4y+14 -0 then use Demoivre's…

A: Given: - If Z=x+iy and the equation is, 4x+y1+ix-4y+i4iy=0 To find: -The value of x and y. Then use…

Q: d²u ²u + əx² ay² 1. to be the form of the solution u? A. u = X(x)T(t) B. a = xt C. u = X(x)Y(y) D. u…

A:

Q: Let u(x, t) be solution of Utt - Uxx = Xxt -00 0 u(x, 0) = u(x, 0) = 0, Then u(2, 3) is equal to (a)…

A:

Q: Consider the following IVP: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b Find the solution. A y(x) =…

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

Q: Show that when T(z) = Solve T(z) = ∞o if c = 0 az+b cz+d where (ad - bc #0)

A:

Q: Let d = gcd(a, b). If (xo, yo) is a solution of the linear Diophantince equation ax + by = c, %3D…

A: It is given that d=gcda,b, x0,y0 is a solution of linear Diophantince equation ax+by=c.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: 8. y" - 4y' - 12y = 3e А. 3/7 e %3D В. Зе C. -3/7 et D. -7e

A: Given: Differential equation is y''-4y'-12=3e5tTo obtain the particular integral of the differential…

Q: B. Prove that the given equation is a solution to the given DE: 7. y = Ax + Be* ; (x- 1) y" - xy' +…

A:

Q: Use the separation of variables method to solve 4uxx = Utt, 0 0 U1 (0,t) = u#(2, t) = 0 u(x, 0) =…

A:

Q: The solution for the IVP: -00 %3D u(x, 0) = 2 x u(x, 0) = -e-x O a u(x, t) =x+ -(x+21)-e-(x-20) 4 O…

A: Known fact: For the system, utt=c2 uxx,   -∞&lt;x&lt;∞, t&gt;0ux, 0=fxutx, 0=gx The D-Alembert's…

Q: 3- Prove that y=x is a solution of (x³ + 2x?)y"+ 2xy'- 2y = 0 and hence find the general

A:

Q: 7. For what values of k will the system 2z + ky + z = 0 (k – 1)x – y + 2z = 0 4x + y + 4z = 0 have…

A:

Q: = 3e2x and y,, = x² + 3x are respectively solutions of у" - бу' + 5у -9е2х y" – 6y' + 5y = 5x² + 3x…

A: General solution y(g)= y(h)+y(p)