The differential equation of the family of curve y = ax +b+1, where a, b are arbitrary constant is d²y dx d²y b) a) +y 0 dx с) +y = 0 d) none of these dx O d) a) O b) O c)

Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: If (x, y) moves from (-2, –1) towards (1, 5) for a distance 0.02, then which of the following is…

A: fx,y=exyPoints from−2,−1 towards 1,5 for a distance 0.02

Q: Find the general solution of y " - 7y " + 16y' – 12y =0 given that r = 3 is a root of the…

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Q: For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane…

A: (a) Solve the differential equation as follows: Let p=dxdt, or, x'. Differentiate it with respect to…

Q: り ydy + Axdx =0

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Q: Solve the followi ing

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: (b) In(2x2 + у — 23) %3D х

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Q: y' + E) y = xy? 2

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Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: is D.E xy? dx + (x+y) dy= 0 a- linear b- Exact C- non_linear ( Explain that)

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Q: linear or not linear? 1) dy 1ax +exy = x²4² dx 2) y + e* sinx= x³y² 31 y\nx - x²y = xy! 4) dy + cosy…

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Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

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Q: 12 Consider the DE: x' x, with solutions x = est [3e L4e-2t and x, = a) Verify that x, and x2 are…

A: By finding the wronskian of the solutions

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: ) 3(x+ y) dx + x(x*+ zy + uy) dy - o t.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find y" if y = cot(9x 2r+ 8).

A: Given, y= cot(9x4-2x +8)   To find: y''

Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

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Q: Solve for the higher order DE number 2

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Q: d²u du dx² dt² = ди +2,8u dt [B.C.] u(0,t) = 0, u(π,t)=0 [I.C.] u(x,0) = f(x), du(x,0) dt = 0

A: The wave equation with source ∂2u∂x2=∂2u∂t2+2β∂u∂twith the IC: u(0,t)=u(π,t)=0B.C: u(x,0)=f(x),…

Q: Find the linear approximation of fcn)cn" In n around n=e Using this equation, y = f(a)+f'ca)(n-a)

A: Applying linear approximation we have

Q: FTnd the General/Practical solution FoT +he Following DTFFerentiat equation. {x-9x? + 16x - 144)y?dy…

A: The differential equation is given as x3-9x2+16x-144y2dy=2x2-1e4ydx find the general solution.

Q: 18.) Compute the directional derivative of f in the given ✓ given points P. 3 a) f(x, y, z) = xy² +…

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Q: RAD, DIV, CURL, V², IRECTIONAL DERIVATIVE + yx, v = [y. z, 4: - x), w = [y". z, x²]. (grad f), div…

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Q: Use implicit differentiation to find dy/dx. 18) y cos = 4x + 4y - y sin A)- cos B) sin 4y 4y2 D)-…

A: 18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Q: Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0,…

A: Given: Differential equation y'=2yx. To do : a) Sketch the slope-field for x in [-2, 2 ] and y in…

Q: 3.) dy_x²(1-y) = 0 dx

A: To solve the following 1st Order Linear DE.dydx-x21-y=0

Q: E- Use the chain rule to express dy / dx in terms of x and y: a) y=7+1 and t=2x+1 1 b) y=7+1 and x=…

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Q: dx + (3x²y² + x?y -

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Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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