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- Transform the differential equation -3y + 4y - 4y = sin(at) y(0) = -4 y = -4 into an algebraic equation by taking the Laplace transform of each side. Therefore Y =arrow_forwardSuppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(T).arrow_forwardSOLVE 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_forward
- D. Solve the differential equation using Laplace transform of y" + y = 6sin 2t ; when y(0) = 3 and y'(0) = 1arrow_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_forwardQUESTION 6 solve the differential equation using Laplace Transform y+2y=4te-2 y(0) = - 3 %3Darrow_forward
- Solve the nonhomogeneous differential equations y" + 25y = 18 cos(4.x) + 18 sin(4.x). Do not use the method of Laplace transform in this problem.arrow_forwardFor Problems 12 and 14, use the Laplace transform to solve the given initialvalue problem. The correct answer for 12: 10 te^(-5t) The correct answer for 14: -(1/2)sint + 2cost - (1/2)tcost. Please show how to get the correct answer for 12 and 14. thank youarrow_forwardTransform 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_forward
- Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' 10y' +25y = cos 6t - sin 6t, y(0) = 6, y'(0) = 5 ۵ Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.arrow_forwardSolve (i) (ii) (iii) (iv) and (v)arrow_forwardQ3:- (A) Solve the following differential equation: y³ −3y² + 3y" - y" = x² 1 (B) Find the inverse Laplace transform of the given function: F(S) = - (5² + a²)²arrow_forward
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