In Problems 23–26 solve the given nonlinear plane autonomous system by changing to polar coordinates. Describe the geometric behavior of the solution that satisfies the given initial condition(s).
26.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- 1. Which of the following is a linear equation? (Select all that apply) (a) 12x + y = 19 (c) sin x + 9y = -4 (e) x² – y² = 1 %3D -3x + 4y (b) т %3D —у +2 2х — Зу (d) - (f) VT = y 10 5arrow_forward13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:arrow_forwardFind two linearly independent solutions of 2a?y" – xy' + (5x + 1)y= 0, x > 0 of the form Y1 = x" (1+ a1r + a2x? + a3x³+..) Y2 = x" (1+ bịT + bzx² + b3x³+..) where r1 > r2- Enter T1 a1 a2 a3 r2 = %3D b2 b3arrow_forward
- 5. Given the system X" - ()* 10 2 (a) Find the general solution. (b) Find the solution that satisfies the initial condition (x(0), y(0)) = (0, –7). Report your solution as one vector.arrow_forward15 Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Center (-1, 1/3) (-2/3, 1/3) (-8/9, 1/3)arrow_forwardExample 11.1. Classify the following equations : a²u 22u d²u du du +4. +4 J + 2- = 0 Əxdy oy² ax dy a²u •+ (1 - y²¹). = 0, -∞ < x ∞, -1arrow_forwardty'''+2y''+y'+ty=0 What is the Wronskian of linearly independent solutions?arrow_forwardQ1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x?)dx + (x2 + y²)dy = 0 Q3: Find the shortest line from a point to a plane, justify your answer by calculations. Hint: you can choose any coordinates of the points and equation of the plane. Q4: Design the biggest box (volume) without cover that made from 6m2 of aluminum. Hint: Use Lagrange Multipliers Methodarrow_forward12. (D + 3D + 2) y = xsin 2xarrow_forward1-2x Question 7 What is the x-intercept of the following equation: y= 1/2x+1 A) (-2,0) B. None of the these (-2,1) (0,2) E) (2,0) F (0,-2) Question 8 Create the equation of a ine tinat is oerpendicular to 2x-y=4 andarrow_forward4. Obtain the differential equation of the family of lines passing through the center of the conics described by the equation x2 + 4y² + 2x – 8y +1 = 0. -arrow_forwardx' = 1 х. Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and (-2,-2). 2.5 1.5 1 0.5 -0.5 -1 -1.5 -2 -2.5 3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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