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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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y-4y +5y 4e", y(0) = 2, y'(0) = 7"
Transcribed Image Text:Use the Laplace Transform to solve the given initial value problem
y-4y +5y 4e", y(0) = 2, y'(0) = 7
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- Use Laplace transform to solve initial value problem.arrow_forwardAn equation of the form +2d²y dt2 dy +at dt + By = 0, t> 0, where a and ẞ are real constants, is called an Euler equation. α (a). Let x = Int and calculate dy/dt and d²y/dt² in terms of dy/dx and d²y/dx². (b) Show that one can use the results of part (a) to transform the original equation into d²y dy + (α − 1). dx² + By = 0. dx Observe now that the resulting differential equation has constant coefficients. (c) Show that if y₁(x) and y2(x) form a fundamental set of solutions of the latter equation in part (b), then y₁ (Int) and y2 (Int) form a fundamental set of solutions of the original equation. (d) Using all above observations to solve 1²y" + 4ty' + 2y = 0arrow_forwardUse Laplace transforms to solve the initial value problem. x''+4x'+3x=1; x(0)=0=x'(0)arrow_forward
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