7. For the differential equation (1-2x)y" + 2y' + (2x-3)y=e³ (a) Write the associated homogeneous equation and check that y₁(z) = e² and 3₂(x) = re-² are two linearly independent solutions of the associated equations. (b) Check that yp(z) = −e¯ is a solution of the full equation. (e) Use superposition principle to write down the general solution of the full equation. (d) Use the existence theorem or the Wronskian to find the intervals on which the solution is valid.
7. For the differential equation (1-2x)y" + 2y' + (2x-3)y=e³ (a) Write the associated homogeneous equation and check that y₁(z) = e² and 3₂(x) = re-² are two linearly independent solutions of the associated equations. (b) Check that yp(z) = −e¯ is a solution of the full equation. (e) Use superposition principle to write down the general solution of the full equation. (d) Use the existence theorem or the Wronskian to find the intervals on which the solution is valid.
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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Transcribed Image Text:7. For the differential equation (1−2x)y" + 2y' + (2x-3)y=e
(a) Write the associated homogeneous equation and check that y₁(z) = e² and y₂(x) = re¯
linearly independent solutions of the associated equations.
are two
(b) Check that y(x) = -e is a solution of the full equation.
(c) Use superposition principle to write down the general solution of the full equation.
(d) Use the existence theorem or the Wronskian to find the intervals on which the solution is valid.
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