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- Forward Euler's method with step h > 0 is applied to solve dy (-a + aj)y(x), da where j = -I and a is some positive real constant. Determine for which values of a the method is stable. Give your answer in terms of h.arrow_forwardSolve the exact equation 2xydx + (x² + 3y2)dy=0 with the initial condition y(2) = 1. Write the solution in the form f(x, y) = C such that f(0,0) = 0. Enter the value of the constant C. Answer: 5arrow_forwardDemand for a certain kind of SUV obeys the following equation,D(x, y) = 22,000 − 1 2 √ x − 5(0.6y − 10)3/2 where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars.Suppose that the price of the car and the price of gasoline t years from now obey the following equations:x = 50,200 + 300t, y = 132 + 5 √ t What will the rate of change of the demand be (with respect to time) 3 years from now?arrow_forward
- Use Euler's method with step size 0.3 to compute the approximate y-values y(0.3) and y(0.6), of the solution of the initial-value problem y = −1+3x - 4y, y(0) = -3. y(0.3) y(0.6) = = "arrow_forwardDevise a modification of the method for solving Cauchy-Euler equations to find a general solution for the equation below. (t-2)²y"(t)-11(t-2)y' (t) +35y(t) = 0,t>2 €0. The solution is y(t) =arrow_forwardUse Euler's method with step size h = 0.2 to approximate the solution to the initial value problem y' = (y + 3), y(1) = 1 at the points a = 1.2, 1.4, 1.6, and 1.8. Compare these to the actual values y(1.2), y(1.4), y(1.6), and y(1.8). What do you notice about the difference between the approximated values versus the exact values as the x value increases?arrow_forward
- Obtain a numerical solution of 4y = 2x- 2y using Euler's method with step size equal to (0.5) and y(0) =1. The estimate y(2) is O a. 0.7656 O b. 0.9492 O C. 0.6875 O d. 0.8456 O e. None of optionsarrow_forwardFind the solution: * (1+ y² + xy²)dx + (x²y + y + 2xy)dy = 0 a. 2x – y²(x + 1)2 = C b.2x?y? + (x + 1)² = carrow_forward
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage