1. Given that {1,cos x, sin x} is a fundamental solution set for y" + y'...
1. Find the solution set for each of the following on the interval - 27 x < 2 A. secx = 2 B. 5 sino - 3 = sin - 5 C. 3tan? = 1 D. sinr = cos E sin cos 7 = r = - sin 2. Find the solution set for each of the following on the interval 0 <r <2 A. COSI = cos x B. 2 sinr = sin C. 2 sinx: - sin x...
4. Given that {cos x, sin 2, 1) is a fundamental set of solutions for y" + y = 0, solve the initial value problem with conditions y(0) = 3, y'(0) = 5, "(0) = -4. 4. Given that {coso, sin x 1} is a fundamental set of solutions for y'" + y = 0, solve the initial value problem with conditions y(0) - 3, V'(0) -- 5. "(0) -4
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı = et and y2 = t+1 are a fundamental set of solutions to the associated homogeneous equation. (b) Find a particular solution using variation of parameters.
Eliminate the parameter to sketch the curve: 2 = sin -0, 1 y = cos -0, 20, - <O<a
Find the exact value of the expression cos(sin If sin = sin 2 15 find the exact value of cos(20) Solve sin 2x = cos 2x, where 0 <x<21.
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
Question 6 Solve: (write solution set in interval notation) x-1 x-2 x-x-2 a) <1 b) > 0 X-5
Find all solutions to cos(7a) - cos(a) = sin(4a) on 0 Sa<
Using the identity sin? 0 + cos² 0 = 1, find the value of tan 6, to the nearest hundredth, if sin 0 = -0.62 and 3 < 0 < 27.
Find the exact value of sinſ and cos given that cos x = 3,27 ,270° <x< 360°. [8] 4-cos e 18. cos20-5 cos 0+4 since 1+cos e