A molecule is moving along the x-axis such that at any time t 2 0 (in seconds), its position from the origin is given by s(t) = 2t³ – 21t2 + 72t – 700 feet.

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find d2y/dx2 in terms of x and y. x2y2-10x=1

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: Find the 2nd solution by reduction of order. y" - 4y + 4y=0; y₁ = e²x

A: Here given the differential equation as y''-4y'+4y=0 .......(1) And it's one solution is y1=e2x

Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: A company which produces scooters has revenue (in dollars) given by R = 300x – 0.02x², where X is…

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Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: Ex. Evaluate the JJex*+2xy+y*) dydx when s tep (x²+2xy+y=) dydx when step Size of X = 0-2 and step…

A: Given: fx,y=x2+2xy+y2 Given step size of (say hx) x=0.5 and(say hy) y=0.5 we need to Evaluate…

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

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Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: Find y" from x =t +7, y = 6t -1

A: Answer and explanation is given below

Q: a. Solve f'(8) for y = Vx – 4x-1 + 2x x² – 6x + 9 b.The y'for y = x – 3 c. The f'(3) for y = v3x² +9

A: Given: a) y=x3-4x-1+2xb) y=x2-6x+9x-3c) y=3x2+9

Q: Q2. Find of y = 4x/x + v at x=1? dr

A: We have to find the dydx of y=4xx+x at x=1.

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

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Q: Find d2y/dx2 implicitly in terms of x and y.    x2 + y2 = 4

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Q: х-2 y = at [-1,1] x²+1

A: The given problem is to find interpolating polynomial for the given function and interval using…

Q: 9. Solve for y, showing all work: 12x – 4y = 20

A: Using algebraic operation

Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Use the diffecential equation dy= and the initial condition. y=(9)%3T. Fad funchion of 81.

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Q: 2a V2ax 2ах f (x, у) dydx (a > 0) е. 2ах-х2

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Q: j. f'(2) appears to have a value of

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Q: Find the equation of horizontal asymptote of y=3(0.2^x)+15pi

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: y"- 5y + 4y ez.

A: Use second order ordinary differential equation rules

Q: What is the DE for A(x^2)+Bx+C using elimination of arbitrary constants.

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Q: dy Find the general solution of xy + y² dr x2

A: According to our guideline, we can solve only first question of multiple question.So, here we solve…

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)&gt;0    3t2…

Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

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Q: 3t X : || 1+t³ 3t 2 y 1+t3 t + -1

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Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: y" (t) – y' (t) - 2y (t) = 12t - 6e2t; y (0) = 1; y' (0) = 0 |

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Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

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Q: 9. Find a quadratic function y = ao + a1x + a2x² satisfying y(1) = 1, y(-1) = 2, and y'(1) = 2.

A: put values and make equations then solve

Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

A: