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

Q: Find the 2nd solution by reduction of order. y" - 4y + 4y=0; y₁ = e²x

A: Here given the differential equation as y''-4y'+4y=0 .......(1) And it's one solution is y1=e2x

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: Find the particular solution that satisfies the initial condition. x3y'+2y=e1/x^2, y(1)=e

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Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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

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Q: y = ", ‚ y(xo) = Yo

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: ! Consider the nonhomogeneous DE: y" + y' – 6y = (12 – 16x)e*. - A) Verify that y, = 4xe* is a…

A: The given differential equation is y''+y'-6y =12-16xex. At first we have to verify yp=4xex is a…

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

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

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Q: 11. xy' - y= y23 Answeri: y = (CVx – 1)3

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Q: : Discuss the existence and unique solution for the IVP y'= 3y3, y (0)=0

A: This question is related to Differential Equations

Q: To find a particular solution of the form Yp = u1y1 + u2y2 of a nonhomogeneous DE using the…

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Q: The solution of the nonhomogeneous DE y" – 2y' +1 = 3e3x is y = cqe* + c2xe* + 3x y = cqe2x + c2 +…

A: We need to find the solution to the nonhomogeneous DE y''-2y'+1=3e2x⇒y''-2y'=3e2x-1. The…

Q: 2. Find the particular solution using the initial condition. ry'-y = x,y(1) = 7.

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

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Q: 14.Show that any separable equation M(x)+N(y)y′=0 is also exact.

A: Given: Mx+Nyy'=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

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Q: y" -4y' + 13y :

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Q: 9. (a) Show that the functions r(t) = 3et+ 7e-t and y(t) = 3et+21e-t are solutions of the system I'…

A: Given: 9. a) x(t)=3et+7e-t and yt=3et+21e-t and a system, x'=2x-yy'=3x-2y satisfying the initial…

Q: Find the general solution of æ*y" + x°y = 4x²y= 1 given that yı = x² is a solution of the associated…

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Q: 4) Find the general solution of the 2nd order PDE 2и. - Зи,, +4и, 3D10 6) +** s (3x +2y) answer:

A: Given : 2nd order PDE       2uxx-3uxy+4ux=10                 --------- (1) To find : general…

Q: 28.If the Wronskian of any two solutions of y″ + p(t) y′ + q(t) y = 0 is constant, what does this…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 1. (a) Find a general solution of the following linear system of differential equa- tions. I = 2x1 -…

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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: y" - 4y - 12y = e6t

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Q: Find a general solution of y"- iy'+6y= 0.

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Q: a) Give a particular solution for y" – 2y' + y = 3e*. %3D

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Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: Find the complete solution of the DE y"- y'=4e¯* +3e* with the initial conditions that when x = 0, y…

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Q: Show that y = In (x) is a solution of xy" + y² = 0.

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Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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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: The solution of the initial boundary value problem * U, = 4u, u (х,0) - 0, u, ( x,0) = x(1– x),…

A: Given, utt=4uxx…

Q: Find the explicit solution to the following Using substitution method, find general solution to the…

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Q: Consider the initial value problem (x + 2) y" + with initial condition x 1 5Y' + e²y=x³ y (0) = 7 y'…

A: Given the Initial Value Problem x+2y"+1x-5y'+exy=x3 with given initial conditions. y0=7,y'0=2

Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: The nonlinear system 5a – x3 = 0, x2 – 0.25(sin x1 + cos x2) = 0 has a solution near (, )'. (a) Find…

A: Given: The nonlinear system…

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: Prove that the general solution to L(y)=(x) is y=Yh+Yp

A: Definitions:  yh is a homogeneous solution so, for any yh, Lyh=0.  yp is a particular solution so,…

Q: 2. (a) Use the method of undetermined coefficient to find the general solution of the non-…

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Q: 10. Find the unique solution of the second-order ivp: y" + 16y = 0, y(0) = 2,y'(0) = -2

A: answer is in next step

Q: Yp = Find a particular solution to y" + 5y' + 4y = - 19te³t.

A: Introduction: The differential equation has a particular solution, which is a singular solution of…

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

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Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1).

A: SINCE YOU HAVE ASK MULTIPAL QUESTION, SO WE WILL ANSWRING ONLY FIRST QUESTION.

Q: 5. Given that y =c, +c,x² is a two-parameter family of solutions of xy'"-y'= 0 on the interval (-…

A: GIVEN: y = c1 + c2 x2

Q: Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

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Q: 1 Find the general solution of x'y" +xy' -y= x+1

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