2 imaginary solutions -medhs there dre ho redi #'s that wotk in the Qudtion, ohly imdginary ニx: x2+9=D0 (3)+9=30 gi?+9=0 -9+ 9 = OV 501utions dte X= 3i dhd X=-31 -31)2 +9=?0 9i2+9 =0 -9 + 9 = 0 V > medns +he heldted ghd ph has ho x-ihtercep+s Yニx?+9

Q: Find the Ye neral solution of the eguation. 6y"_5y_4 y =o %3D

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Q: 2. Find the general & particular solution of the DE, 4- 16 + 16y = 0 with the given that y(0) = 2…

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Q: Using the Green's 2nd identity, prove that for 2-D Neumann exterior problems, O(In r) 09 Inr-0 dl .…

A: Consider the Green's second identity, ∭Du∆v-v∆udv=∬∂D=u∂v∂n-v∂u∂nds From the equation consider the…

Q: a) Show that U = e-x sin (nt) is a solution to a²u = 0. %3D ax2 at2

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Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: 3)- find ahe pr patikular solustien of theditfrential equatisnx+Cx =CL given the x6)=a Ax 20 at t=o…

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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: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: 'ind the Wronskian of any pair of solutions to 2t?y" + 3ty' – y = 0,t > 0.

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Q: What is the general solution of rydx (2² + 3y²) dy = 0 ? %3D 6y² In y = C O + 6y² In y = Cy² %3D

A: Given: xydx-(x2+3y2)dy=0

Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

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Q: dx -2xcsc 2y – 2x³cos 2y dy sec 2y

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Q: What is the general solution of (2xy + y) dr + (r? - r) dy = 0? %3D C(z 1) * y = Cr(z - 1) * O y =…

A: Given differential equation is variable separable differential equation of first order. We will…

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: D. Verify if The relatum O y= xe' y= eco{ 2x) is a soluhon to yl-Gy'+13y=D0 is a solution to yl -…

A: For verification of the solution will find the respective derivative and substitute into the…

Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: Suppose that z'y"+ azy' + by = 0 has the general solution of the following form: y = C23 + C,r³ In…

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Q: 47. Prove that the imaginary part of the solution of z" + z' + z = te' is a solution of y"+y' +y=t…

A: Given,                           z''+z'+z=teit                                 (1)

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: uppose j = ce (:) + 2etz 2 1 5x cze# ) 1 4x is the general solution to y = Aỹ %3D 1 What is A ? 1

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Q: 1. (3x – 2y + 1) dx + (3x- 2y +3) dy = 0, %3D Ans. 5(x + y+ c) = 2 In | 15x - 10y + 11L

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Q: 3. ® Find the genelal Solution of the differentral egation (D'+ 25) y = cscX Sinx t Sin 5X cos 3X

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Q: What is the general solution of zyda - (2 +3y) dy = 0 ? O a + oy In y Cy og In y = C 6y Iny cy? Quiz…

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Q: 5. Find the particular solution of D' + 3D° + 2D° ]y=0 provided that when x = 0, y = 0, y' = 4, y" =…

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Q: rks) Find the solution of the following problem: Utt = 9uzz, x > 0, u(x, 0) = x², u(x, 0) = 6x +3,…

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

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: [5] Use the Gaussian quadrature to approximate the integral 1 x²e¬*dx. (a) Choose n = (b) Choose n =…

A: As per instruction we are allowed to answer only two sub questions. The generalised Gaussian…

Q: Find length of the cardioid r=a0³from 0 = 0 to 0 = n %3D

A: Length of the cadioid is given by below formulaLength = ∫0πaθ3dθ

Q: Consider the Taitral value problem b-)y (0)=1 what con you say about the existence ond uniqueress of…

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Q: 33 prone that ucx, y) = x F(2x+y) is a general %3D Solution of x Ux-2xUy = Ucxyy) then find the…

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Q: What values of α and A make y=Acos⁡αt a solution to y″+2y=0 such that y′(1)=3? α= A=

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Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Q: It is known that the two basic solutions of y" +b (x equation y" + b (x) y' +c(x) y = f (x) we use w…

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Q: Find a one parameter family of solutions of the following separable equation: dy 74 - 4 12r2 – 6e3r…

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Q: The DE whose general solution has the form y= C + C2x+ C3x² + Cgx³ 1s given by Od 4) = 0. %3D e.…

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Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: The position of a moving particle is given by s = 5 + 9t- t on the interval 0 <t <5, then its…

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Q: 36. Given that dy + 2y = () and y = 1when = 0. A dr quadratic approximation for y is A 1- 21 – 21 B…

A: We have given a differential equation.  We have to find a quadratic approximation for y

Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: What is the general solution of xydx (22 + 3y2) dy = 0 ? - %3D 22 + 6y2 In y = Cy? %3D Gylny = cy?…

A: To find  The general solution of the given differential equation.

Q: What is the general solution of xydx (22 + 3y?) dy = 0 ? - 6y² In y = C 2 + 6y? In y = Cy? 6ylny cy?…

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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: 5] The particular solution of ( Dª ( D³ – 2D² + 3D – 6)y = –16 is 8. 8. (a) Yp= (b) Yp= x* (c) Yp=…

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Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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Q: The general solution of the DE y" + 4y' = 0 where y(0) =1 and y'(0) = 8 is O None of these OF y = 3…

A: OPTION (b) IS CORRECT. THE GENERAL SOLUTION IS  y= 3-2e-4x

Q: - 15x = 3r³t is a de dt (Choose all applicable answers.) O Homogeneous equation O Exact cquation O…

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