Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation 3y" + p(t)y/ + q(t)y = g(t), provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t) and show that y satisfies equation 38 if v (38) is a solution of Y1(t)v" + (2y4 (t) + p(t)y1(t))v' = g(t). (39) Equation 39 is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 5t², t > 0, yı(t) = t. NOTE: Use c1, C2, for the constants of integration. ... y(t) =
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Transcribed Image Text:The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation 3y" + p(t)y/ + q(t)y = g(t), provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t)y1(t) and show that y satisfies equation 38 if v (38) is a solution of Y1(t)v" + (2y4 (t) + p(t)y1(t))v' = g(t). (39) Equation 39 is a first order linear equation for v'. Solving this equation, integrating the result, and then multiplying by y1(t) leads to the general solution of the first equation. Use the method above to solve the differential equation ty" – 2ty + 2y = 5t², t > 0, yı(t) = t. NOTE: Use c1, C2, for the constants of integration. ... y(t) =
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