1 dz, C:k – 3i] = 3 z² +4z + 13

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

A: We have given a differential equation and we have to find substitution to make it variable…

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: What is the point of intersection of the given DE (x + 2y – 1)dx – (2x + y – 5)dy = 0 ? Select the…

A: Given,  DE : (x+2y-1)dx-(2x+y-5)dy=0

Q: z 3e*3S,y 3z2 + sin(z)s G dx

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Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: Given z = 2t -41 and y=4 sin t %3D dy (i) da dy (ii) da?

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: If yo is the particular solution of dy 4x y, y(0) = 3, dx find the value of yo(2).

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Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: xy dA, where D = {(x,y) | sin x <y < 1/2,0<

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Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: If yo is the particular solution of dy 4x°y, y(0) = 3, %3D %3D dx find the value of yo(2).

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Q: Consider the DE d?y dy + - 6y = 12x, y(0) = 1 - dx? dx 1 is a solution of the DE and determine 3…

A: y=Ae2x-2x-13 Differentiating with respect to x, we get dydx=A·2e2x-21-0   ∵deaxdx=aeax, dxndx=nxn-1…

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

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Q: dz Given z = 4x2 + y²,x = sin t, y = t2, find : dt

A: Topic = Derivative

Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: dy Find a solution of x dx y2 - y that passes through the indicated points. (a) (0, 1) y = | 0

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Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

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Q: fz? +z+1 I = dz co

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Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

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Q: What is the general solution of (D² – 2D + 5) y = 0 ? - y = Cie + C2e3 %3D y = Cie cos 2x + C2e sin…

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Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: Solve the DE by Variation of Parameters (D³ + D° = 2D) y = 4e¯= cos z -2x COs I y (0) = 0.4, y' (0)…

A: The differential equation is D3+D2-2Dy=4e-2xcos x with the initial condition y0=0.4, y'0=-0.4,…

Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: yit yä - 2xyzk b. V= xy Sin Z (i +2+ e)

A: Please check step 2 for the solution.!

Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: dy Find -5 y%3D(2+cos4t) dy dt

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Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: (b) [₁³ sin (π(x – 2y)²) dA, where T is the triangle bounded by x – 2y = 1, y = −3x and 5y = -x.

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Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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