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Differential Equations: An Introduction to Modern Methods and Applications
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- Question 2. Solve the following initial value problem (DO NOT use Laplace transform method): +y-4- 4y=3e-4-6 x=// 10=0 70=2arrow_forwardConsider the differential equation 2y"+ ty'-2y = 14, y(0) = y'(0) = 0. In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{ft)} and n = 1, 2, 3,..., then L{"{t} = (-1)F(s), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Ys) = Lly(t)}. Solve the first-order DE for Y(s). Y(s) =| Then find y(t) = Z (Y(s)}. y(t)%Darrow_forwardplease be handwrittenarrow_forward
- Figure 1.5.8 shows a slope field and typical solution curves for the equation y' = x + y. (a) Show that ev- ery solution curve approaches the straight line y = -x – 1 as x → -00. (b) For each of the five values yı = -10, -5, 0, 5, and 10, determine the initial value yo (accurate to five decimal places) such that y(5) = yı for the solution satisfying the initial condition y(-5) = yo- 10 6. 2 -10 -5 FIGURE 1.5.8. Slope field and solution curves for y' = x + y.arrow_forward2- Solve the fractal differential equation Day + y = 5e²x - 1²/23 and y(0) = 1, Using Laplace transform With aarrow_forwardpart c is the only incorrect answerarrow_forward
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