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For Problems 7–21, verify that the given function is a solution to the given
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Differential Equations and Linear Algebra (4th Edition)
- Are the functions f, g, and h given below linearly independent? f(x) = e2" + cos(7x), g(æ)= e2 – cos(7x), h(x) = cos(7x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (e2z + cos(7x)) + (e2z – cos(7x)) + (cos(7x)) = 0. help (numbers)arrow_forwardA solution is yp(x)=arrow_forward3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.arrow_forward
- Are the functions f,g,f,g, and hh given below linearly independent? f(x)=0, g(x)=cos(8x), h(x)=sin(8x) If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.arrow_forward4. Determine constants a, b, c, d and e that will produce a quadratic formula Lf(x)dx = af(-1) + bf (0) + cf(1) + df'(-1) + ef'(1) %3Darrow_forwardC. Eliminate the arbitrary constants in each equation and express the final answers in the following form: a,n(x)y(n) + an-1(x)yn-1) + . .. + a1(x)y' + ao(x)y – g(x) = 0 . 1. r* – y² = cy 2. y = cje" + cze²" + c3e*rarrow_forward
- 1. Obtain the differential equation having the solution as the equation representing all parabolas with vertex and focus on the x-axis opening to the right.arrow_forwardIf y = x² - xy + 1, then when 0-1/1/201 01/1/20 0-1 0-2 O nonexistent -1, dis =arrow_forwardIf L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333 , then b=arrow_forward
- 3. Find the differential equation of a family of parabolas with axis parallel to the y-axis.arrow_forwardA chemistry student heats a beaker that is at room temperature (30 ° C)by inserting it in an oven that has been preheated to 250 °C. If u is the temperature of the beaker in °C, what is the appropriate equation to model the temperature of the beaker. O du/dt = k(u –- 250) O du/dt = k(u – 30) O du/dt = k(250 – u) O du/dt = k(30 – u)arrow_forwardIf x/4 = y/3 = z/2, then what would be the value of (5x + y – 2z) / 3yarrow_forward
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