T f(2,v) de dy = K, where K is a constant, then 72 f(x, y) dy| dæ = If O 72K O - K ок O - 72K

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

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Q: dw dw and ds 3 Assume that w =f(s° +t) and f'(x) = ex. Find dw at dw do II

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Q: t+1 dy If x = and y = t2 - 2t +3, then find t-1 dx

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Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

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: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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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: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: ²+ re" = 2y + e² %3D

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Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: d²y 1 dy y + y(3) = 0.009u, y(10) = 0.003s - dt2 t dt Use an appropriate method to find y(t).

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what…

A: Given query is to find indicated derivative.

Q: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

Q: b) d²y + 5y = 2t, given that y = 0 and = 1 when t = 0 dt dy %3D dt2

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Q: d'y dy dt Find the solution to the IVP + 9- + 18y = 0 where y(0) = - 7, (0) = 33. dt2 y(t) : Preview

A: Given that  The differential equation is  To find the solution of differential solution at given…

Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: z=9x + 4y + 1 dy = (9x+4y+ 1) 2 reduces to dx Using the substitution the DE -- dz=9dx+ 4dy

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: z = In (VT" + y") If With n e N, n > 2, Then the result of 2 (dz dy dz n Corresponds to: "-1 + y"-1…

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Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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Q: If f(x,y) = e* cos y then fyy (0,) is fyy (0) is

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: + y = e In t 16. 2y" + 2y' + y = 4Vx 17 3x" 6y' + 6y = e* sec r

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Q: 5. Evaluateſ, x²y dx + xy² dy where C is given by: r(t) - 3t v(t) – et 0<t< 1

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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: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: dy 4) 0 and y > 0 dt dy 5) > 0 when both t >0 and y < -t dt

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

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 fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

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Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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Q: ex+y+Z If f(x, y) = x+ey+e²> then the %3D ex+eY +eZ > value of fx + fy + fz is equal 2f f

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Q: dt (b) z = x?y where x = st and y = t2 – s2 dz 2st?(t? – s?)? – 4s³t²(t? – s²) as answer: az 2s²t(t?…

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Q: dz (5) If z = u² + v² and u = at², v= 2at, find dt

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Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

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Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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Q: dr if r = s+1 and s = dt s = 161? – 20t . Find - d²y Find if y=x +3x - 7 and x= 2t +1. dr d'y t if x…

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Q: If f(x, y) = 2x2 – 9y, then the total differential of f at x = 1 and y = -2 is : O df = 4 dx - 36 dy…

A: Given: fx,y=2x2-9y2 To determine: The total differential of f at x=1 and y=-2.

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following