Find the differential equation of families of ellipse with center at the origin. a. xyy" + x(y')² — yy' = 1 b. xyy" — x(y')² — yy' = 1/2 c. xyy" − x(v¹)² + yy' = −1 d. xyy" + x(y')² + yy' = 2 e. Not in the list
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- Find the differential equation of the family of ellipses with center at the origin a and the major axis on the y−axis.Which is the differential equation of the family of ellipse with center at the origin and major axis along the y-axis.4. Form the differential equation representing the family of hyperbola having the center at the origin and the foci on x-axis.
- Which is the differential equation of the family of parabolas with axis along the y-axis and with a distance "a" from the vertex to the focus. A. xy² - g': B. y" - xy' =c c. xy² - y =o D. x²y" -y²=0 = y² - x^²y² = 0 =03 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x') 2(y') 2 = 4 (x') 2 - (y') 2 = 8 (x') 2 - (y') 2 = 4The differential equation of the family of hyperbolas with horizontal transverse axis and with asymptotes 2x +- 3y = 0 is given below. Find A and B.
- 4. obtain the differential equation of the family of plane curves describe and sketch several representative members of the family. Parabolas with vertex and focus on the x-axis.Find all the singular points for the differental equation and classify each as regular or irregular. Dont slove the equation. (x2+x-6)y'' + (x +3)y' + (x-2)y = 0(2) Find the coordinates of the points of intersection of the parabola y = x' and y =x+3.
- 2.b) Eliminate the Arbitrary Constants in the equation: * x²y = 4 + Cy x?y = 4 + y' x?y" = -4y Ob. a. xy? – 2y' = 0 y = -4y C. d.Solve for y: (z2y''+zy'-1)y - z2(y')2 = 02. Find the differential equation of the family of ellipses having center at the origin and such that the major axis is always equal to 3 times the minor axis and whose directrices are always perpendicular to x – axis. Sketch some of the family of curves.