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d) d'y dy dx² dx - - 2y = 5e²x

d) d'y dy dx² dx - - 2y = 5e²x

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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**Solve the equation using the method of undetermined coefficients.** a) \(\frac{d^2y}{dx^2} - 2\frac{dy}{dx} - 8y = 2e^x\) b) \(\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 2 + x^2\) c) \(\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 3\cos(2x)\) d) \(\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 5e^{2x}\) e) \(\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 2e^x\) f) \(\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + 2y = 2 + 3\sin x\) g) \(\frac{d^3y}{dx^3} - y = 2e^x\) h) \(\frac{d^3y}{dx^3} - 2\frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 2 + e^{2x}\) These differential equations can be solved using the method of undetermined coefficients. This method is particularly effective for linear differential equations with constant coefficients. The approach involves assuming a particular form for the solution based on the type of non-homogeneous term and then determining the coefficients by substitution into the original equation.
Transcribed Image Text:**Solve the equation using the method of undetermined coefficients.** a) \(\frac{d^2y}{dx^2} - 2\frac{dy}{dx} - 8y = 2e^x\) b) \(\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 2 + x^2\) c) \(\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 3\cos(2x)\) d) \(\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 5e^{2x}\) e) \(\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 2e^x\) f) \(\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + 2y = 2 + 3\sin x\) g) \(\frac{d^3y}{dx^3} - y = 2e^x\) h) \(\frac{d^3y}{dx^3} - 2\frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 2 + e^{2x}\) These differential equations can be solved using the method of undetermined coefficients. This method is particularly effective for linear differential equations with constant coefficients. The approach involves assuming a particular form for the solution based on the type of non-homogeneous term and then determining the coefficients by substitution into the original equation.
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