(1 point) Match the following guess solutions yp for the...

(1 point) Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. yp(x) = Ax^2 + Bx + C, B. yp(x) = Ae^2x, C. yp(x) = A cos 2x + B sin 2x, D. yp(x) = (Ax + B) cos 2x + (Cx + D) sin 2x E. yp(x) = Axe^2x, and F. yp(x) = e^3x(A cos 2x + B sin 2x) 1. A d^2y/dx^2 + 4y = x - x^2/20 2. E d^2y/dx^2 + 6dy/dx + 8y = e^2x 3. C y'' + 4y' + 13y = 3 cos 2x 4. D y'' - 2y' - 15y = e^3x cos 2x

Transcript

00:01 Hello everyone here the given problem is in this first part we have d square y divided by d x square plus 4 y this is equal to x minus x minus 1 squared divided by 20 so the auxiliary equation is auxiliary equation is m square plus 4 this is equal to 0 so the value of m square this is minus 4 and from here the values of m this is equal to plus minus 2 a aorta so from here the value of y c c this is equal to c1 cost 2 x plus c2 sine 2 x and so the value of yp, this is equal to ax square plus bx plus c.

01:14 So here which option is our correct option? option a is our correct option.

01:19 And in the second part, here this is d square minus 60 plus 8 into y.

01:28 This is equal to e raise 2 to 2x.

01:31 So here the auxiliary equation is, auxiliary equation is, m square plus 6m plus 8 this is equal to 0 so we can factor of this quadratic equation so the factors are m plus 4 into m plus 2 so this is equal to 0 from here we can find the values of m so m is equal to minus 4 and m is equal to minus 2 so the values of y see this is equal to c1 e raised 2 power minus 2 x plus c this m here is minus 4 so this is e rase 2 power minus 4 x so the values of y p this is equal to a into e raise 2 power 2 x so which option is our correct option b option is our correct option and the third part is third part is in this the auxiliary equation is m square plus 4m plus 20 this is equal to 0 from here we can find the values of m so the m is equal to minus 4 plus minus root of b squared minus 4 ac so here the b square is 16 and minus 4 ac is 80 divided by 2 a here the values of a is 1 so this is 2 then m is equal to minus 4 plus minus 8 aorta divided by 2 so after divided we will get here minus 2 plus minus 4 aota so the values of y c this is equal y c this is equal to a raise 2 power minus 2 x into c 1 cos 4x plus here 4x the term with iota this is 4 so here we take 4x and here this is c to sine 4x then the yp this is equal to a so here this is sine a sine 2x plus b cos 2x here which option is our correct d option and the values of yp, this is also the value of yp, this is equal to a cost 2x plus b, sine 2x...

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