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6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a

6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a

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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4/5: Please solve the following differential equations marked with a red circle.
4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. 2e³t5e-t, y₂ = 11e-t (b) y₁ = cos(πt), y₂ = =sin(at) (c) Y₁ = e2t cos(5t), y2 = e²t sin(5t) (d) y₁ = e³t, y₂ = te³t (a) yı = 5. Find the general solution of the equation xy" + 2y + xy = 0, if we know that y₁ = solution. COS X X is a
Transcribed Image Text:4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. 2e³t5e-t, y₂ = 11e-t (b) y₁ = cos(πt), y₂ = =sin(at) (c) Y₁ = e2t cos(5t), y2 = e²t sin(5t) (d) y₁ = e³t, y₂ = te³t (a) yı = 5. Find the general solution of the equation xy" + 2y + xy = 0, if we know that y₁ = solution. COS X X is a
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