Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2. Select one: a. False b. True

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dt…

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Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

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Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

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Q: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: Using u = 1 + t°, the limits of integration will change from t = 0 to u = and from t = 1 to u =

A:

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. dy…

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Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

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Q: Let y 5x + 6x + 2. If Ax = 0.2 at x = 1, use linear approximation to estimate AY Ay =

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Q: Let y = 5x + 7x + 3. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay =

A: Follow 2nd step.

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: Assume w = x2y4, where x and y are functions of t. Find dw>dt when x = 3, dx>dt = 2, dy>dt…

A: Given:  w = x2y4, x and y are functions of t  To Find: dw/dt when x = 3, dx/dt = 2, dy/dt = 4, y = 1

Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: 5x + 6x + 2. If Ax = 0.2 at x = 1, Let y = approximation to estimate Ay use linear Ay =

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Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху

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Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

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Q: Let y = 5x + 3x + 4. If Ax = 0.1 at x = 5, use linear approximation to estimate Ay Ay =

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Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

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Q: Let y(t) satisfies dy dt 3ty-t-t 1+t2 for t2 0, and y(t = 0) = 1. Show that y(t) S 1+t for t2 0.

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Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: Find dw/dt at t 1 if w xe + ysinz - cosz, r ! = 2/t, y = t – 1 and z = nt.

A: v

Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: Find y', where t (a) y = Jo dt VE2 +1 (b) y /t² +t+1 dt 1 • sin²3x (c) y = | 1 dt t2 +1 Cos x

A: The given function is: y=∫cos xsin2(3x) 1t2+1 dt

Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: (1, y' + 5y = f(t), y(0) =0, where f(t) = 0st<1 %3D t21

A: Solve the intial value problem using Laplace transferoms

Q: Find dy/dt if y is as follows. t2 + 4 y = In 7 - t dy dt II

A: We use logarithmic properties to simplify the given function and use chain rule to solve this…

Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

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Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt when x = 4. dy…

A: we will diferenciate the equation of y with respect to t, and solve this.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.