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Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. help (equations) Enter the derivatives as y', y", ... (b) Find the general solution to this differential equation. help (equations) In your answer, use C₁, C2, C3 and C4 to denote arbitrary constants and x the independent variable. Enter c₁ as c1, c₂ as c2, etc.

Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. help (equations) Enter the derivatives as y', y", ... (b) Find the general solution to this differential equation. help (equations) In your answer, use C₁, C2, C3 and C4 to denote arbitrary constants and x the independent variable. Enter c₁ as c1, c₂ as c2, etc.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. help (equations) Enter the derivatives as y', y", ... (b) Find the general solution to this differential equation. help (equations) In your answer, use C₁, C2, C3 and C4 to denote arbitrary constants and the independent variable. Enter c₁ as c1, c₂ as c2, etc.
Transcribed Image Text:Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. help (equations) Enter the derivatives as y', y", ... (b) Find the general solution to this differential equation. help (equations) In your answer, use C₁, C2, C3 and C4 to denote arbitrary constants and the independent variable. Enter c₁ as c1, c₂ as c2, etc.
Help Entering Equations Equations must have an equals sign and use the correct variable names: y = 5x+2 will be incorrect if the answer is w = 5y+2 Examples of valid equations that are equivalent: 32= 5*x + 2 is the same as 30= 5x or x = 6 y = (x-1)^2+3 is the same as y 3 = (x-1)^2 x^2 + xy + y^2 = 13x is the same as y* (y+x) = 13x - x^2 • If there is no equation that solves the question: Enter NONE OF DNE (this may vary from problem to problem) Examples of constants used in equations: pi, e e^1 • Functions may be used in equations, but may not be applied across the equals sign: sqrt(x) = sqrt (5) is valid, but sqrt(x=5) is not • Link to a list of all available functions
Transcribed Image Text:Help Entering Equations Equations must have an equals sign and use the correct variable names: y = 5x+2 will be incorrect if the answer is w = 5y+2 Examples of valid equations that are equivalent: 32= 5*x + 2 is the same as 30= 5x or x = 6 y = (x-1)^2+3 is the same as y 3 = (x-1)^2 x^2 + xy + y^2 = 13x is the same as y* (y+x) = 13x - x^2 • If there is no equation that solves the question: Enter NONE OF DNE (this may vary from problem to problem) Examples of constants used in equations: pi, e e^1 • Functions may be used in equations, but may not be applied across the equals sign: sqrt(x) = sqrt (5) is valid, but sqrt(x=5) is not • Link to a list of all available functions
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