Question

please solve this differential equation problem in mathematica

Lab 2 Exercise Use the Basic Math Assistant palette -Advanced for your functions. eall trig functions: Sin[expr, Cos[expr], Tan[espr], Sinh[epr and In(x) will be Log[x] expr Determine whether the given set of functions are linearly dependent or independent on (-) <-2, f2(x) x3, f3(x) = 5x 2. f1(x) Cos[2x], f2(x) Sin[2x], f3(x) Cos[x]*Sin[x] 3. f1x) e, f2(x) = e*, f3(x) Sinh[x] 4. f1(x) Cos[2x], f2(x)= x, f3(x) = (Cos[x])^2,f4(x) = Sin[2x] 5. Given the Nonhomogeneous DE: 2x2y 5xy +yx2-x General Sol 'n: y Clr12. C2x1xx on (0, ) 1. f1x) Show linearly independent for the complimentary solution. Show that y is a solution to the DE by using DSolve. a. b.

Answer 1

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NET tb eus2nt Isin 2 ksinixe632 26032x -16sinx eos2x + 16 e Cos2x +16sinn cos2u + Sinzx 32 K Sin2L -32%sh2 +0+ 16c0s 2 32 CasY - 16 #0 - 16 (1+ cos2 x) = 16 c0s2 w(5, S2,3,S4) = -16 0 Syfeife Su are Liveary ind epedat. a) Here Now 8 olutions are indnpeudeut (6) C 2 + 2 2 2 29 4 2 (P Proed 2 Now el 2 C2 +