y'dy 3 (4–v’) 2

Q: Express the general solution in terms of Bessel functions: z²y" + 4xy/ + (x² + 2)y = 0

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Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: S(2- sec2x) elmale sec³x sec(3A – x) e ln (xle) What should be the value of A for dr to be…

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Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: The integral ₁₁x – y dxdy is equal to: Select one: 0 O2 O None of them -2

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Q: dy de Xoy. -Secxy)

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Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: Given dy dy dz² +2 + 5y = e dr and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the…

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xcos2y dx + tany dy = 0

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Q: dy – 5x-2+ 2x-1 – 6; y(1) =7. dx |

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Q: 1. Solve the DE as follows: d'y dy +3 +2y = 24 y(0) = 10 and y'(0) = 0 di? dt

A: Given differential equation  is   y"+3y'+2y =24    ;    y(0) =10     , y'(0) =0

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: The DE: dY - 4xy +5y² xy + 3x? can be transformed into a seperable DE dx in x and z by using the…

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Q: dy _ 4xy+5y² can be transformed into a seperable DE The DE: dx xy +3x2 in x and z by using the…

A: The solution is given as

Q: 4хy + 5y? xy +3x? in x and z by using the substitution y = xz dy = can be transformed into a…

A: We will use the substitution to try to transform the given differential equation into separable…

Q: Solve the equation by Cauchy's integral formula. ez dz z - 5

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Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: we solve thd DE y dx 2x0y-0aer convedding it to oad sing an integrating tactor, then the solution…

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Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: Calculate . (x² + x²)e²as, where S is the cylinder with equation x² + y² = 9 for 0 < z < 10.

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Q: S B+1F dx (Improper Integral) (3x+1)?

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Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: -2 2x Jo x2-4 Só dx (Improper Integral)

A: Let I is the value of given Integral.

Q: dy x®y – 23x²y? 8' is a first ord 4,,5 x*y° + 3y° – 8x homogeneous equation dx Select one: True…

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: - (7- dy sin2x ) dx = 0 y y

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Q: Evalate jsinty)hube where 2 05ys1,05xsy. a) 1-cos(r) b-costr)) 9-cosd) osd) d) 1-cos(l))

A: Change of variables:             ∫x1x2∫y1y2f(x,y)dy dx=∫y1y2∫x1x2f(x,y) dx dy.

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: Which of the following is NOT true about the DE: 6x²ydx +2x*dy=0?

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: Find the general solution of the following IVP: (32²tany + 2) + (x³ sec?y – 1) = 0, y(0) = 0. %3D dz

A: Simplify the differential equation to exact form and integrate each terms.

Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry ln² y + yln y)dr + (2x² In y +…

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: 4. Find dy and Ay for y = 3VT-1+2x at r = 2 with dr = Ar = 0.2. %3D

A: The given equation is y=3x-1+2x. Given that x=2, dx=△x=0.2. Now,…

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: Solve the following DE, using Separable method. y'In ly| +x*y =0.

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Q: Solve this DE by Separable method  1. (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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

A: 2. We need to determine the solution of the differential…

Q: Solve the DE: (1+ y?) dæ + (x²y + y) dy = 0 O Not Exact DE Exact DE

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