In each of Problems
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
Additional Math Textbook Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Thinking Mathematically (6th Edition)
Introductory Statistics
Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics
Precalculus: Mathematics for Calculus (Standalone Book)
- 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_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_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_forward
- How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.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_forwardSolve (i) (ii) (iii) (iv) and (v)arrow_forward
- 4. Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x²). %3|arrow_forwardWhen the Laplace transform is used to solve the IVP: y'+5y=314, y(0) = 2 the following equation is derived SY(s) + Y(s) = $$ +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
- Consider 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_forwardFigure 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_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education