WebFrom y2 = kx3 we get k= y2 x3. Substituting, dy dx = 3· y2 x3 · x2 2y dy dx = 3y 2x This equation gives the slope of the original family at any value (x,y). Then the slope of the orthogonal (perpendicular) line must be dy dx = − 2x 3y and we solve this differential equation to get the equation for the family of orthogonal trajectories. dy ... WebThis is the Solution of question from Cengage Publication Math Book Calculus Chapter 6 DIFFERENTIAL EQUATIONS written By G. Tewani. You can Find Solution of ...
x^2 - 2(y^2) = 10*y orthogonal trajectories - Wolfram Alpha
WebFeb 4, 2024 · Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. x^2 - y^2 = k Show more. WebMar 3, 2024 · This suggests a method for finding orthogonal trajectories of a family of integral curves of a first order equation. Finding Orthogonal Trajectories. Step 1. Find a differential equation y ′ = f(x, y) for the given family. Step 2. Solve the differential equation y ′ = − 1 f(x, y) to find the orthogonal trajectories. caravan parks in bright vic
Find the orthogonal trajectories of the family of curves: …
Web5. Find the orthogonal trajectories of the family of curves y 5 = k x 2. I start by knowing that I need a differential equation satisfying all members of family, which means k needs to be eliminated. Differentiating both sides with respect to x: y 5 = k x 2 5 y 4 d y d x = 2 k x Replacing k 5 y 4 d y d x = 2 y 5 x 2 x 5 y d y d x = 2 x d y d x ... WebVIDEO ANSWER: We have to find Art O'connell trajectory of X square plus four Y square which is equal to K. It's equal to zero, which is eight way the way by the X. It's equal to two wigs. We didn't order as equation too four because the Y by D X was. ... Find the orthogonal trajectory: x2 + 4y2 = k. WebQ: Find a parametrization for the cylinder x2 + y2 = 1. A: Click to see the answer. Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant. A: Given surface is 9x2+4y2=30 and plane is 9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…. Q: Find a parametrization for the cylinder ... caravan parks in bright