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Often a radical change in the form of the solution of a differential equation corresponds to a very small change in either the initial condition or the equation itself. In Problems 39‒42 find an explicit solution of the given initial-value problem. Use a graphing utility to plot the graph of each solution. Compare each solution curve in a neighborhood of (0, 1).
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forwardIn Problems 27 – 36 solve the given initial-value problemarrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 4. x" + 25x = 90 cos 41; x (0) = 0, x'(0) = 90arrow_forward
- In Problems 43–46, solve each equation on the interval 0 ≤ θ < 2π43. sin(2θ) + sin (4θ) = 0 44. cos(2θ) + cos(4θ) = 0 45. cos(4θ)) - cos(6θ) = 0 46. sin(4θ) - sin(6θ) = 0arrow_forwardI. Classify each differential equations in terms of order, degree, dependent variable,independent variable, ordinary or partial, and linear or non-linear. If non-linear, state theterm where it is non-linear.arrow_forward2. Verify that the indicated function is a solution of the given differential equation.arrow_forward
- 3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.arrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 1. x" + 9x = 10 cos 2t; x(0) = x'(0) = 0arrow_forwardIII. Solutions of Differential Equations. Verify the followingarrow_forward
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