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In Problems 11-40 verify that the indicated function is a solution of the given differential equation. Where appropriate, c₁ and c₂ denote constants. 11. 2y' + y = 0; y = e = x/² 12. y' + 4y = 32; y = 8 dy 13. - 2y = e³x; y = e³x + 10e²x dx dy dt 15. y' = 25+ y²; y = 5 tan 5x 14. + 20y = 24; y = -e-20r

In Problems 11-40 verify that the indicated function is a solution of the given differential equation. Where appropriate, c₁ and c₂ denote constants. 11. 2y' + y = 0; y = e = x/² 12. y' + 4y = 32; y = 8 dy 13. - 2y = e³x; y = e³x + 10e²x dx dy dt 15. y' = 25+ y²; y = 5 tan 5x 14. + 20y = 24; y = -e-20r

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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In Problems 11-40 verify that the indicated function is a solution of the given differential equation. Where appropriate, c₁ and c₂ denote constants. 11. 2y' + y = 0; y = e-x/² 12. y' + 4y = 32; y = 8 dy 13. - 2y = e³x; y = e³x + 10e²x dx 14. dy dt 16. + 20y = 24; y = -e-20r 15. y' = 25+ y2²; y = 5 tan 5x dy dx y y = (√x + ₁)², x > 0, ₁ > 0 17. y' + y = sin x; y = sin x - cos x + 10e* 18. 2xy dx + (x² + 2y) dy = 0; x²y + y² = C₁ 19. x² dy + 2xy dx = 0; y = 2 20. (y')³ + xy' = y; y = x + 1 21. y = 2xy' + y(y')²; y² = c₁(x + 1/ c₁)
Transcribed Image Text:In Problems 11-40 verify that the indicated function is a solution of the given differential equation. Where appropriate, c₁ and c₂ denote constants. 11. 2y' + y = 0; y = e-x/² 12. y' + 4y = 32; y = 8 dy 13. - 2y = e³x; y = e³x + 10e²x dx 14. dy dt 16. + 20y = 24; y = -e-20r 15. y' = 25+ y2²; y = 5 tan 5x dy dx y y = (√x + ₁)², x > 0, ₁ > 0 17. y' + y = sin x; y = sin x - cos x + 10e* 18. 2xy dx + (x² + 2y) dy = 0; x²y + y² = C₁ 19. x² dy + 2xy dx = 0; y = 2 20. (y')³ + xy' = y; y = x + 1 21. y = 2xy' + y(y')²; y² = c₁(x + 1/ c₁)
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