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Equations with the Dependent Variable Missing For a second-order differential equation of the form y" = f (t, y'), the substitution v = y', v' = y" leads to a first-order equation of the form v' = f(t,v). If this equation can be solved for v, dy = v. Note that dt then y can be obtained by integrating one arbitrary constant is obtained in solving the first-order equation for v, and a second is introduced in the integration for Y. Use this substitution to solve the given equation. (1+t²)y" + 2ty' + 27t-² = 0, y(1) = 18, y'(1) = -9 %3D y(t) =

Equations with the Dependent Variable Missing For a second-order differential equation of the form y" = f (t, y'), the substitution v = y', v' = y" leads to a first-order equation of the form v' = f(t,v). If this equation can be solved for v, dy = v. Note that dt then y can be obtained by integrating one arbitrary constant is obtained in solving the first-order equation for v, and a second is introduced in the integration for Y. Use this substitution to solve the given equation. (1+t²)y" + 2ty' + 27t-² = 0, y(1) = 18, y'(1) = -9 %3D y(t) =

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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Equations with the Dependent Variable Missing For a second-order differential equation of the form y" = f(t, y'), the substitution v = y', v' = y" leads to a first-order equation of the form v' = f(t, v). If this equation can be solved for v, dy = v. Note that dt then y can be obtained by integrating one arbitrary constant is obtained in solving the first-order equation for v, and a second is introduced in the integration for y. Use this substitution to solve the given equation. (1+t²)y" + 2ty' + 27t-2 = 0, y(1) = 18, y'(1) = -9 y(t) =
Transcribed Image Text:Equations with the Dependent Variable Missing For a second-order differential equation of the form y" = f(t, y'), the substitution v = y', v' = y" leads to a first-order equation of the form v' = f(t, v). If this equation can be solved for v, dy = v. Note that dt then y can be obtained by integrating one arbitrary constant is obtained in solving the first-order equation for v, and a second is introduced in the integration for y. Use this substitution to solve the given equation. (1+t²)y" + 2ty' + 27t-2 = 0, y(1) = 18, y'(1) = -9 y(t) =
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