Determine the Linearity of this DE. * ay dy ニ X Linear O Non-Linear

Q: For the ODE dy = y² – 3y dt find a(yo) for Yo < 0 O 00 -V3 O V3

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Q: A. Expand, that is, perform the indicated operations on the differential operator D. 1. xD(D + x) 2.…

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Q: (у — х + хусot x)dx + xdy 3D 0

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Q: Transform rydy = y²dx + ydy into a separation variable form. dr ydy = 0 %3D O de dy : = 0 x-1 fip O…

A: Solving the problem by the said method.

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Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

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Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

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Q: Let x = s e and y =t es. Compute the Jacobian

A: Given: x=set and y=tes.

Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: b) Let X = Cle,e+ 2] and define T:C[e,e+2] → R by re+2 T(z) = | 1(t)dt, r€ Cle,e+2] Show that T is…

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Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

Q: t (s? + t) ds – s (s² – (s² – t²) dt = 0 %3D - 242 In Let|

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

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A: Given : f(x) = x2   x0 =  9

Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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Q: iv) if zy = (x)- then zx + Zy = %3D %3D

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Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

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Q: Find general polutien yoy! + x = 0 of followoing eeparable obts. ODES. a. y' = e*** yz 2メー1 b. = e²

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Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Find the general solution of the DE dyldx = y(x – y) /x^2. O y = C/ In(y) O y = C/ In(x) O y = x /…

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Q: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: + (xytl) Determine the Linearity of this DE. * ya dy y dy O Linear O Non-Linear

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Q: dw Use an appropriate form of the chain rule to find dt In(14.x² – 4y + 523); x = ti, y= tổ, z = t-2…

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Q: By using Green's Theorem, evaluate the integral (1+xy') dx +x²y dy, where R is the closed R path…

A: From the given problem:   I=∫R1+xy2dx+x2ydy   From Green's theorem:   ∫F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy…

Q: Find the linear approximation of fcn)cn" In n around n=e Using this equation, y = f(a)+f'ca)(n-a)

A: Applying linear approximation we have

Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

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Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: To find the linearization Lx,y,z of the function at the given points fx,y,z=x2+y2+z2 at 1,0,0

Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: 6y" – 5y' + y = 0, y(0) = 4, y'(0) = 0

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Q: 2. Let z = g(x, y) = e" cos y + y In(x – 1). %D Use local linear approximation to estimate g(1.99,…

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Q: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Give the family of orthogonal trajectories of y' = Cx + 5. a) O x² + y² – 10y¯' = c b) O x² + y² +…

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Q: linear or nonlinear.

A: A PDE is said to be linear if the dependent variable u and all its partial differential coefficients…

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: Thelem:-TP PTR har ociva bveof %eI,theu f is Coutivlalse- at Xo CTs thecouvese of thevem triue?why?

A: Questions from continuity and differentiability

Q: F the generl solution of y=2 by reduing itto a frust order ODE the depandant vaiable the indepandurt…

A: y''=2 integrate both sides with respect to x y'=2t +c1 c1 is the integration constant Integrate on…

Q: (a) Prove that d θν θ E) - e, de ди дө dw a0 - dt ax ax dt ax ax Әх ду Әх др given that + u- + v -+w…

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

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Q: (a) z = 1– In y (b) 22 = 1. Show the traces as well.

A: Given a) z=1-ln(y) b) x29+y24+z2=1