Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show that 4vo v(1) = (kt /0o + 2)²

Q: Obtain the solution using Integrating Factors Found by Inspection y(x3y3 + 2x2 − y)dx + x3 (xy3 −…

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Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: Supply the missing integrand and the limits of integration sinx dy dx _dx |1– y²

A: Solution is given below:

Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: 3(1 + 2) - dy 2ty(y – 1) dt

A: The method to find the solution of the differential equation helps to find the required solution.…

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A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: w =sec (xyz) - Yx +y+z

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Q: Reverse order, then integrate SaE ) dydx. Vx \1+

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Q: dy 2. sec²y secx dx ;y(0)=0

A: The given differential equation is dysec2y=dxsecx and y(0)=0

Q: Obtain the solution using Integrating Factors Found by Formulas a.)  xydx − (x2 + 2y2)dy = 0

A: I am attaching image so that you understand each and every step.

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: Find the total differential. z = 2x6y9 dz

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: Solve by Laplace transforms. y – 3 | y(T)dr = 4e' sin(2t). %3D 0,

A: by Applying Laplace transformation and inverse Laplace transformation we get the answer

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: Find temperature in a rod with length L=2 and: Ut = 4uxx u(0,t) = 1,u(2, t) = 3 0 < x <1 u(x,0) =…

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Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: 1. xy + z2

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Q: Find the total differential. z = 5x3y8 dz =

A: The solution is:

Q: Evaluate the deflection of a vibrating string of unit length having fixed ends with initial velocity…

A: Consider the wave equation    ∂^2u∂x2=1c2∂^2u∂t2     .....(1)   here U(x ,t) is the defection of the…

Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: Find the total differential of  w=x3yz+xy+z+3

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Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: Find the solution of the differential equatlor dy 3xeY, y(0) = 0 dx %3D

A: Consider the equation

Q: Give the integrating factor for 3((y^4)+1)dx+4x(y^3)dy=0. (in terms of x)

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Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: Find the total differential. w = e3Y cos(5x) + z5 dw

A: The total differential of a function w= f(x,y,z) with continuous first partial derivatives in a…

Q: X Cos 9TTX² dx 2. 2. V= dTx²

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Q: Find the total differential. z = 10x6y7 dz =

A: Differentiation of xⁿ = nxn-1

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

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Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: Find the total differential. z = 6x *y5 iz

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Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

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Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: What is the integrating factor of the nonexact DE (4xy + 3y – x) de + æ (x + 2y) dy = 0?

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