17. Find the solution of the separable DE 2ydy = (x² + 1)dx. a. y = E+x+C +x +C 3 b. y =+x+C c. y = x3 + x + C d. y = x³ + 3x +C

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: y" + 2y' – 3y = 0

A:

Q: Show that the equation x2 + y2 = 2003 has no solutions in theintegers.

A:

Q: 6) The largest interval in which the solution of the initial value problem et (cost)y" +ty 5 %3! t-3…

A: y''+p(t)y'+q(t)y=r(t), given initial value at t0 This equation has unique solution in the interval…

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 7x2 +…

A: Here we have to find ode of given solutions

Q: 7 Find the second linearly solution of the D.E x'y"+xy'-(x+2)y = 0, given that: y,(x) =

A:

Q: 2. Find the solution u = u(x, y, t) of the following initial value problen Un + yu, + 4xuy = -u²,…

A: We solve this equation by Partial differentiation method: The given equation is ut+yux+4xuy=-u2 We…

Q: Find the general solution of dy -my – ny³ dt by making a suitable substitution that transforms the…

A: Differential equation

Q: 1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (wheret is a real constant)

A: Explanation of the solution is given below....

Q: Find a particular solution to y" + 5y' + 6y = lte".

A:

Q: Find the largest t-interval such that a unique solution of the following initial value problem is…

A:

Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

A:

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: Use the separation of variables method to find the solution of IBVP du du at ax² 0≤x≤4, 120 Subject…

A:

Q: Solve the nonhomogeneous IVP using the method of undetermined coefficients: y" +4y = x - 2cos 2.x,…

A: To solve the given Homogenous IVP using the method of undetermined coefficients.

Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: 1. Consider the DE dy dz dy -5- + 4y = 8x + 2, y(0) = 1 dr Verify that y = Ae + 2x + 3 is a solution…

A:

Q: Let y = e2x and y2 = e3x be solutions for a homogeneous DE. Then, %3D is also a solution to the DE.…

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: 1. Find the particular solution of the DE y" -11y' + 24y = 0 subject to the boundary conditions y…

A: The differential equation can be solved as follows:

Q: What is the largest interval on which the following initial value problem is guaranteed to have a…

A: I am sending the explanation in written format, kindly adjust. I have written the answer in detail,…

Q: Find the general solution of (d²s)/(dt²) + 2(ds/dt) + 5s = 0. OA.y = C₁e(t) cos2t + C2 e(t) sin3t…

A: Let's solve given diffrential equation.

Q: 2nd Case (IBVP Summary) (Ut = 1.5uxx, 0 0 Ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0<…

A:

Q: 3. Find for the simplified general solution of (1 + x³)dy – x²ydx = 0 a. Iny =In(1 + x³) + C b. Iny…

A:

Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: Solve for the particular solution of the following non-homogeneous DE. y” – y’ = 2sin 2x

A:

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

A:

Q: If q x2 yz3 %3D =, the small increment in q with &r=8y=8z=±0.1 can be approximately calculated by…

A: We will use partial derivatives to calculate the required quantity.

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

A:

Q: +2. =0 by Find the solution of the PDE dx? dy² variable separable method

A: Given problem is :

Q: Solve the ODE x²y" + xy' +| y = 0 about a singular point 16

A: We need to solve ODE.

Q: Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy…

A: We will find Jacobian matrix  for system of differential equation Then depend on eigen values of…

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: * السؤال .8 The homogenous D. E. with constant coefficient of at least order which has the solution…

A:

Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

A:

Q: The solution to the non-homogeneous DE y' - Бy +ву 3D2х + 3 is 2. a. Ae3x + Be3* +1/3 x + 7/9 b.…

A:

Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

A:

Q: 23 3. Determine whether the function y(x) = 2sin4x is a solution to the initial value problem of y"…

A:

Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: 2. Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) =Q

A:

Q: The solution of the nonhomogeneous DE y" + 4y' +4=5e* is

A:

Q: 12. Obtain the general solution of (D4 + 16D² + 63)y = 0 a. y = c,cos 7x + c2sin v7x + C3 cos 3x +…

A: D4+16D2+63y=0D4+0D3+16D2+0D+63y=0auxillary equation is m4+0m3+16m+0m+63=0Put…

Q: 13 By direct partial integration, Solve the following PDES s. 8²u ахбу = CEX COSysXu(X,t) Ex UCH, y)…

A:

Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý - y = e*

A:

Q: Find the particular solution of the DE y " -11y + 24y = 0 subject to the boundary conditions y (0) =…

A: Given y''-11y'+24y=0  ; y(0)=2  and  y'(0)=-3

Q: 12. Obtain the general solution of (D4 + 16D² + 63)y = 0 a. y = c,cos v7x + c2sin /7x + c3 cos 3x +…

A:

Q: 6. Find the particular solution of 2xydx + (y² – x²)dy = 0 ;where y = 2 and x =

A:

Q: Find the general solution of the DE dyldx = (x + y) / x. O y = (x^2)ln(Cx) O y = (x^3)ln(Cx) O y =…

A:

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

A:

Q: Find the particular solution of the separable DE with the given boundary condition. e ; when x-0 and…

A: