) Use the d'Alembert solution to solve = 2 -00 < x < o0, t> 0, 1 u(x, 0) = e, u(x, 0) : 1+ x2*

Q: Find a particular solution to the IVP given by: y" + 2y" - y' - 2y = 0, y(0) = 1, y'(0) = 2, y"(0) =…

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Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

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Q: (c) Using the method of characteristics, or otherwise, find the general solution to Uy +5Ux = 0.

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Q: Solve for the particular solution of the following non-homogeneous DE. y” - 4y' - 12y = e6t

A: Explanation of the answer is as follows

Q: Find the solution of x²y" +5xy' +(4+4x)y=0, x > 0 of the form n =1,2,3,... where co 1. Enter r = =…

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y()= 3x?y² becomes +z(-÷) =…

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Q: ck that y(x) = e rx with r satisfying ar 2

A: Introduction: Introduction: In mathematics, differentiation is the process of determining the…

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

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Q: Find the general solution of i = Ax, where A = .

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Q: 7. Show that y(t) = c,e¬# +czte¬2# is a solution to y" +4y/ +4y = 0. Determine the constants c and…

A: The given equation is y"+4y'+4y=0. A second order linear, homogeneous ordinary differntial…

Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

Q: 2²y" - 4.xy+6y= 0, y(2)=0, y'(2) = 4 %3D

A: The differential equation is given as x2y''-4xy'+6y=0x2D2y-4xDy+6y=0x2D2-4xD+6y=0 It is a Cauchy…

Q: It was stated in the text that, if R, L, and C are positive, then any solution of LI" + RI' + I/C =…

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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: Solve for the particular solution of the non-homogeneous DE. 2y'' +y' = 3

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Q: 3. 2y" + у' - 3 А. 3 В. Зх C. 3x D. x?

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Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

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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: 2 11 3. x*y" – 5xy'+9y= 2x

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Q: No type answer

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Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

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Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁u₁v) = 0 (uv₁ - u₁v) =…

A: We know, if u and v are the two solutions of d2ydx2+Pdydx+Qy=0 then Wronskian of…

Q: Find the approximate solution of the equation Uxx = 4u; by Crank- Nicolson method subject to u(x, 0)…

A: Given: The equation uxx=4ut Initial and boundary conditions: ux,0=0, u0,t=0 and u2,t=2t   To find:…

Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: Solve the below equations by Gaussian elimination metho- x +z = 1, 2x +y+z 0, x+y+ 2z = 1

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Q: 2y" + y' = 3

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Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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

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Q: 4(a)Verify that the equation y = Inx – Iny is an implicit solution of the TVP, ydx = x(y+ 1)dy y(e)…

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Q: Find the solution of Uy = 36 ut + 10 u if Ux U₂ (x,0) = 3e-2t using the method of separation of…

A: Given partial differential equation is ux=36ut+10u____(1) and given condition isux(x,0)=3e-2x We…

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

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: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

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

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Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: If one was to use Euler's method to solve  u′(t)=−u(t)2,u(0)=1 and y′(t)=2−y(t),y(0)=1 for…

A: The slope of the tangent for u at 0 is: u'(t)=-2*1=-2,It is Negative. So, f is concave upwards, so…

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.

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Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

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Q: d²y dy 7t- + 5y = t2 – 2 dt PVI = dt2 dy y(1) = 2; (1) = 1 dt

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Q: |Given that y, = t? is a solution to the DE t'y"- 3ty' + 4y 0 on (0, 00), use reduction of order to…

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