Can someone please help me solve 9,15,17 9. Given that y = ce' cos x + ce sin x is a two-parametersolutions of y" - 2y' + 2y = 0 on the interval (-∞,00), determinewhether a member of the family can be found that satisfies the condi-tions(a) y(0) = 1,(c) y(0) = 1,10. Given that y =of xy" - 5xy'y'(0) = 0y(π/2) = 1(b) y(0) = 1,y(t) = -1(d) y(0) = 0, y(T) = 0₁² +₂²¹ + 3 is a two-parameter family of solutions+ 8y = 24 on the interval (-∞, ∞), determine whethera member of the family can be found that satisfies the conditions(a) y(-1) = 0, y(1) = 4(b) y(0) = 1, y(1) = 2y(2) = 15(c) y(0) = 3, y(1) = 0(d) y(1) = 3,In Problems 11 and 12 find an interval around x = 0 for which the giveninitial-value problem has a unique solution.11. (x - 2)y" + 3y = x; y(0) = 0, y'(0) = 112. y" + (tan.x)y=e*; y(0) = 1, y'(0) = 013. Given that y = C₁ cos Ax + C₂ sin Ax is a family of solutions of the dif-ferential equation y" + ²y = 0, determine the values of the parameterÀ for which the boundary-value problemy" + x²y = 0, y(0) = 0, y(π) = 0has nontrivial solutions.14. Determine the values of the parameter À for which the boundary-valueproblemy" + A²y = 0, y(0) = 0, y(5) = 0has nontrivial solutions. See Problem 13.4.1.2 Linear Dependence and Linear IndependenceIn Problems 15-22 determine whether the given functions are linearly inde-pendent or dependent on (-∞, ∞).15. f(x) = x,f(x) = x²,16. f₁(x) = 0,f₂(x) = x,17. fi(x) = 5,f₂(x) = cos²x,f(x) = sin²x18. f(x) = cos 2x, f(x) = 1,f3(x) = cos²x19. f(x) = x, f(x) = x - 1, f3(x) = x + 320. fi(x) = 2 + x,f₂(x) = 2 + |x|21. f(x) = 1 + x,f₂(x) = x, f(x) = x²22. fi(x) = et, f2(x) = ex, f(x) = sinh xf3(x) = 4x - 3x²f(x) = exIn Problems 23-28 show by computing the Wronskian that the given functions are linearly independent on the indicated interval.23. x¹, x²; (0, ∞)24. 1 + x, x³; (-∞∞)

9. Given that y = ce cos x + ce sin x is a two-paramet solutions of y" - 2y' + 2y = 0 on the interval (-∞,0), determine whether a member of the family can be found that satisfies the condi- tions (a) y(0) = 1, (s) y(0) = 1 y'(0) = 0 Y(π/2) = 1 (b) y(0) = 1, (d) y(0) = 0, y() = -1 y(T) = 0 of coluti.

9. Given that y = ce cos x + ce sin x is a two-paramet solutions of y" - 2y' + 2y = 0 on the interval (-∞,0), determine whether a member of the family can be found that satisfies the condi- tions (a) y(0) = 1, (s) y(0) = 1 y'(0) = 0 Y(π/2) = 1 (b) y(0) = 1, (d) y(0) = 0, y() = -1 y(T) = 0 of coluti.

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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