A particular curve passes through (1, 1) and satisfies the differ- ntial equation dx = (1-3y²³) dy. Find an equation of the curve in the form rh(u).

Q: (7) Find the lengths of the curve r =2/(1 - cos 0), a/2<0<n.

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Q: Which indicates the derivatives of parametric equations? *

A: Solution: Option D Derivatives of a Parametric function:  x = g(t) and y = f(t)  dxdt= g'(t), dydt=…

Q: dy y = x-'(a² + x²)¿, solve for dx

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Q: CALCULATE USING A HOMOGENOUS EQUATION. GIVE THE GENERAL AND PARTICULAR SOLUTION. SOLVE NUMBER 3 THE…

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Q: x = e' – 1, y = e", 2t -0 <t < Eliminate the parameter to find a Cartesian equation of the curve.…

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Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: Find parametric equations for the tangent line to the given curve at the point (30, 135, 469). The…

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Q: Show that the following equations are exact. Find solution. (a) dx dy_x– y³ + y² sin x 3xy² + 2y cos…

A: (a) The differential equation is given as dydx = x-y3+y2 sinx3xy2+2y cosx It can be rewritten as…

Q: Find P.S. of (16x +5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-3)

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 1.) Find the derivatives of a.) y = 3e²x — 2lnx + arcsec x

A: the given equation is

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

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Q: Consider the curve 6+2xy + y³ = 4 The equation of the tangent line to the curve at the point (1, 1)…

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Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

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Q: dy Find of the equation Arcsin(x +y) + y = x² dx

A: To find dydx of the equation, arcsinx+y+y=x2

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

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Q: x(t)=sin2((pi/2)-t)  y(t)=cos4((pi/2-t) 0≤t≤pi/2 determine the slope of the curve at t= pi/4…

A: xt=sin2π2-t,  yt=cos4π2-t,  0≤t≤π2 Differentiating with respect to t, we get dxdt=2sinπ2-t·ddtπ2-t…

Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: Consider the implicit curve C defined by the equation C: ln(²+1) + ln(y² + 1) = In 5. dy da dr dy'…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: classify by type, order and linearity the following equation (1-x)y"-8xy'+6=cosx

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Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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