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12. x² sin(x + y) = 1, -

12. x² sin(x + y) = 1, -

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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F4 % 5 T FS ^ 6 8. y = 3 sin 2x + ex, In Problems 9-13, determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 9. x² + y² = 4, 10. yIn y = x² + 1, 11. ey + y = x-1, 12. x² sin(x + y) = 1, 13. sin y + xy - x³ = 2, Y y" MacBook Air F6 & 7 14. Show that (x) = c₁ sin x + c₂ cos x is a solution to d²y/dx² + y = 0 for any choice of the constants c₁ and C₂. Thus, c₁ sin x + c₂ cos x is a two-parameter family of solutions to the differential equation. Ad F7 15. Verify that (x) = 2/(1-ce), where c is an arbitrary constant, is a one-parameter family of solutions to * 8 DII FB y" + 4y = 5ex 6xy' + (y')³sin y-2(y')² 3x² - y 1 ( dy dx dy dx dy dx dy dx - O 9 DD F9 X O y = 2x sec (x + y) - 1 2xy y - 1 exy-y exy + x ) - O 7 F10 P F11 11. + F12 20. 21. 22. delete
Transcribed Image Text:F4 % 5 T FS ^ 6 8. y = 3 sin 2x + ex, In Problems 9-13, determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 9. x² + y² = 4, 10. yIn y = x² + 1, 11. ey + y = x-1, 12. x² sin(x + y) = 1, 13. sin y + xy - x³ = 2, Y y" MacBook Air F6 & 7 14. Show that (x) = c₁ sin x + c₂ cos x is a solution to d²y/dx² + y = 0 for any choice of the constants c₁ and C₂. Thus, c₁ sin x + c₂ cos x is a two-parameter family of solutions to the differential equation. Ad F7 15. Verify that (x) = 2/(1-ce), where c is an arbitrary constant, is a one-parameter family of solutions to * 8 DII FB y" + 4y = 5ex 6xy' + (y')³sin y-2(y')² 3x² - y 1 ( dy dx dy dx dy dx dy dx - O 9 DD F9 X O y = 2x sec (x + y) - 1 2xy y - 1 exy-y exy + x ) - O 7 F10 P F11 11. + F12 20. 21. 22. delete
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