3. A) f(t) = (t + 4)° %3D B) L s° +43

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: Given z = 9t – 11 and y = 81 sin t %3D dy (i) dz dy (ii) dx?

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Q: (2y – 3x)dx +xdy = 0 %3D

A: Find your answer below

Q: I am having trouble evaluating ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above…

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Q: 1 In (a² + y? + 1) dædy -VI-y? |

A: I use polar conversion method to solve this double integral

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: The radius r and height h of a right circular cylinder are related to the cylinder’s volume V by the…

A: It is given that, the height (h), radius (r) and volume (V) of a cylinder are related by the…

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

A:

Q: Determine the solution of the following homogeneous DE: sec (G) -y ]dx +xdy

A: Given differential equation is x secyx - y dx + x dy = 0

Q: d?y What is the degree of the DE dy 3 dz 2 dx A 3 2 1/2

A: Degree: the degree of the differential equation is defined as the exponent of the highest order…

Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

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Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

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: 3- show that the diff. equ. is homogeneous and Solve it (2x +34) dx + (y-x)dy = 0

A: To find the solution of the given differential equation(DE).

Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: If f(z, y) = e" sin(4y) then: V f( – 1, 1) =

A: Given function is f(x, y) =e4xsin4y.  We have to find ∇f(1, -1 ). The vector differential operator ∇…

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

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Q: Given y = Vx³ + 1, evaluate dy using delta process. dx

A: Given y=x3+1evaluate dydx using delta processSolution fx=x3+1 dydx=fx+dx-fxdx  dydx=x+dx3+1-x3+1dx…

Q: The differ ential equation 2 y e =0 is b. Linear homogeneOUS d. separable

A: The differential equation is given by y4x+2y'ex = 0 To evaluate : The type of differential equation.…

Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

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Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Use Cramer's Rule to solve the system.

A: 13x-15y+12z=710-23x+25y+32z=1110x-45y+z=95 Here,…

Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking h = 0.5, 3 the value…

A: Given integral: ∫36x2dx h=0.5 To find: the value of N=?? [no.of sub-intervals]

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: What is the numerical approximation to -dx -1 2+x using the basic trapezoidal rule? (a) 0 (b) 2 (c)…

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Q: Find the yacral Selution Sulution 2. d 2. dy +y=D0

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Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: Solve the homogeneous DE. 4. y? dx + x(x + y)dy = 0

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y? y dy +

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy +y dx = 3x?y? becomes dz…

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Q: T(z, Y, 2) = 1500e 2y

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Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: Solve the DE shown below, with boundary condition y(1) = 1. (1 Point) %3D xdy - (4y + x')dx 0

A: GIVEN EQUATION IS LINEAR DIFFERENTIAL EQUATION.

Q: If z'y +y = r dy 1, then at (0,-1) is

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Q: uct Theorem. 10. K y KM=

A: Solution

Q: given FCX)= x° t use definatron Of desivative

A: Given: fx=x2+1x Definition of derivative: f'x=limh→0fx+h-fxh