Concept explainers
To fill: The blank in the statement, “The only solution of the initial-value problem
Answer to Problem 1CR
The only solution of the initial value problem
Explanation of Solution
Theorem used:
The existence of a Unique Solution:
For a nth order initial value problem
If
Calculation:
Consider the initial value problem
Compare the equation to the standard form of differential equation
Note that,
The initial value
By the existence of unique solution, the general solution of the initial value problem
Therefore, the only solution of the initial value problem
Want to see more full solutions like this?
Chapter 3 Solutions
Advanced Engineering Mathematics
- A Moving to another question will save this response. Question 11 Find the general solution of Xy" + xy -4y 0 where y(1) =0 and y (1) = 4arrow_forward6. Solve the following Euler's equations: (a) x²y" +5xy' + 4y = 0 (b) x²y" - xy + 3y = 0arrow_forwardQUESTION 3 . 1 1 a) Find the general solution of y" -=y'+- x2 --= (0arrow_forward
- Example 9.13. Solve Yr+1-Yx + x +Yx = 0 given y₁ = 2.arrow_forwardSolve the equations in Exercises 1–5 by the method of undetermined coefficients. 1. y′′ - y′ - 2y = 20 cos x 2. y′′ - y = ex + x2 3. y′′ + y = 2x + 3ex 4. y′′ + 2y′ + y = 6 sin 2x 5. y′′ - y′ - 6y = e-x - 7 cos xarrow_forwardMoving to the next question prevents changes to this answer. Question 9 Which of the following equations has a solution of the form F(t,y) = C. A. 3t + 2y + (3t+ 2y)y' = 0 B. 3t+ 2y + (3y + 2t)y' = 0 O A. A only O B. B only OC. A and B O D. None A Moving to the next question prevents changes to this answer.arrow_forward
- Zad. 2. Give an example of a differential equation whose solutions are functions of the form y(t)=t+c√1+t².arrow_forwardQuestion 2. Given that y₁ = x ¹/2 cos(x) is a solution to the equation x²y" + xy' + (x²-y = 0. Apply the reduction of order method to find a second linearly independent solution and the write the general solution of the above equation.arrow_forwardQuestion 1 Eliminate the constants of the equation below: y = c;e* + c2xe* A y" - 2y' +y = 0 B y"-y'+y = 0 y" - y' + 2y = 0 (D y"+2y' +y 0arrow_forward
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,