In Problems 11–16 verify that the
16.
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- 11arrow_forwardThis is the first part of a two-part problem. Let O 21 P = -2 sin(2t)] -2 cos(2t)]* cos(2t) y1(t) sin(2t)| ÿ2(t) = a. Show that 1(t) is a solution to the system i' = Pý by evaluating derivatives and the matrix product O 2] -2 Enter your answers in terms of the variable t. b. Show that y2(t) is a solution to the system i' = Pj by evaluating derivatives and the matrix product %(t) y2(t) Enter your answers in terms of the variable t.arrow_forwardThis is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181arrow_forward
- of the form y₁ = (1+₁+ a₂²+az³ + ...) 3₂ = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter Find two linearly independent solutions of 2x²y" - xy + (2x+1)y=0, z>0 T1 1 01 = a₂= 03 = T2= 1/2 b₁ = b₂ = b3 =arrow_forwardS sec2(3 – 2t)dtarrow_forwardIf y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.arrow_forward
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