Match the solutions to the differential equations. If multiple options could be
ID: 3119547 • Letter: M
Question
Match the solutions to the differential equations. If multiple options could be correct for one of the differential equations, pick the option that includes all solutions. These answers are correct, but I would like to understand why. Neat work would greatly be appreciated. Thanks!
(1 point) Match the solutions to the differential equations. If multiple options could be correct for one of the differential equations, pick the option that includes all solutions 12y 9y 2. yl 3. T y A. y or C. y D. y or y orExplanation / Answer
1. Just substitute eac hof the answers into the qequations and and you will have the answers.
Forexample, for 1st equation, you know that a 12 coeffiecnet has to come with the 1st term.
Therefer, e^kx answers will not do, we have to get something like 4*3 , whic is option E.
2. Second one has to a 3*3. So, x^kx are ruled out, e^kx are in.
A is the only option with this, hence is the answer
3. The answer should have even number when differentiated as 2nd and 4th term have even numbers.
A , is ruled out therefore. D and C also won't work as it doens't sum up 0
Subbing D, x^2 *12x^2 -2x*4x^3 -4x^4= (12-8-4 )*x^2 = 0, this works. D is the answer.