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Chapter 5 Solutions
DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
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- SOLVE D.E. USING LAPLACE TRANSFORMS. x'(t) – 3x"(t) – 4x'(t) + 12x(t) = 12e-t ; x(0) = 4 , x'(0) = 2 , x"(0) = 18 Answer: x(t) =e-t+ e3t + 2cosh(2t)arrow_forward4. Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x²). %3|arrow_forwardSolve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution. y''+y=2u(t-4); y(0) = 0, y'(0) = 4 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.arrow_forward
- Transform the differential equation -2y + 4y = cos(at) y(0) = -6 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y. (not Y(s)). Therefore Y =arrow_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_forward2- Solve the fractal differential equation Day + y = 5e²x - 1²/23 and y(0) = 1, Using Laplace transform With aarrow_forward
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