Fundamentals of Differential Equations (9th Edition)
9th Edition
ISBN: 9780321977069
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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Solve 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 x
Solve the equations in Exercises 1–16 by the method of undeterminedcoefficients.
y'' - y' - 6y = e-x - 7 cos x
For each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution.
Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that.
Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.
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- Solve the equations in Exercises 1–16 by the method of undeterminedcoefficients. y'' + y = cos 3xarrow_forwardIn Problems 71–80, solve each equation on the interval 0 ≤ θ < 2πarrow_forwardProblem. 9: Let z = x? 7 xy + 6 y? and suppose that (x, y) changes from (2, 1) to (1.95, 1.05 ). (Round your answers to four decimal places.) (a) Compute Az. (b) Compute dz. ?arrow_forward
- 1. Describe and solve each first-order equation. (a) x²y'=xy²+3y² (b) y'+3y=3t²e-³tarrow_forwardA4 Locate the singular points of the equation x(x − 1)²y" + 2y + xy = 0, and determine whether or not these are regular.arrow_forwardIn Problems 1–6, find all values of the given complex power. 1(-1)* 2. 32i/# 3. (1+i)'-i 4. (1+v3i)' 6. (ei)v2 5, (-i)*arrow_forward
- 6. Solve the following Euler's equations: (a) x²y" +5xy' + 4y = 0 (b) x²y" - xy + 3y = 0arrow_forward. Find the general solution to y" + 6y" + 13y' = 0.arrow_forward4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (2) (x² D² + xD – 41)y = x2arrow_forward
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