PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric equations given. 1. x = 1+t² , y = 4t – 3 2. x = t2 – 1 , y = t² + t
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- 1. Find the differential equation of the family of plane curves described. Draw at least three members of the family. All tangent lines to the parabola x^2=4y 2. (xy-6xy^2)dy - (2y^2-9xy)dx when x=1 , y =1In each exercise, obtain the differential equation of the family of plane curves described. 1. The trisectrices of Maclaurin y2(a+x)=x2(3a-x) In geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. ps; I need complete solutions Thank you and God bless :)The function y(x) is defined by the parametric equations {x=t2+t+1y=t3−2t. Find the differential of the function at the point (3,−1).
- Obtain the differential equation of the family of plane curves describe and sketch representative members of the family. 1. Parabolas with vertex on the x-axis with axis parallel to y-axis and with distance from focus to vertex as a The answer is a(y')^2=y. Pls Show solutionObtain the differential equation of the family of plane curves described and sketch several representative members of the family. Sketch the graph. 1. The cissoids r = a sin θ tan θ. (See Exercise 29 for the equation)Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1.Parabolas with vertex on the x-axis, with axis parallel to the y-axis, and with distance from focus to vertex fixed as a. Ans. a(y')^2=y 2. Parabolas with vertex on the y-axis, with axis parallel to the x-axis, and with distance from focus to vertex fixed as a. Ans. x(y')^2= a
- Obtain the differential equation of the family of plane curves described,and sketch several representative members of the family. 1. family of lines with slope and x-intercept equal 2. family of parabolas with horizontal axis and with distance from vertex to focus fixed as a Write complete solutions and box your final answers.Obtain the differential equation of the family of plane curves described and sketch several representative members of the family. 1. Parabolas with axis parallel with the y-axis and with distance from vertex to focus fixed as a. Ans. 2ay"=1 2. Parabolas with axis parallel to the X-axis. Ans.y'y'''-3(y")^2=0Form the first-order differential equation y=e^{(\sin y+x)} . Form the first-order differential equation of e^y=sinx Form the second-order differential equation using the parametric definition of y=a sinθ,x=a cosθ
- Obtain the Differential Equation of the family of plane curves. 3. The trisectrices of Maclaurin y^2(a+x)=x^2(3a-x). Show solution, sketch and pls write in a legible hand writtingWhat does the differential equation dr/dθ=0 represent in polar plane? 1. A family of spirals 2. A family of exponential curves 3. A family of parallel straight lines 4. A family of circlesBessel parametric equation: Use variable substitution (z=λx) and determine a set of solutions for the differential equation: x2y''+xy'+(λ2x2-v2)y=0