Mathematics: The given two-parameter family is a solution of the indicated differential equation on the interval (−[infinity],[infinity])(−[infinity],[infinity]). y=c1.ex. cosx+c2.ex.sinx ; y′′−2y′+2y=0 Determine whether a member of the family can be found that satisfies the boundary conditions. a. y(0)=1, y (pi)=0 b. y(0)=1, y(pi)=-1 c. y(0)=1, y(pi/2)=1 d. y(0)=0, y(pi)=0

The given two-parameter family is a solution

Karolina0304

29.01.2022

I do 1 option for you as an example, you need to check the leftover by yourself.

Step-by-step explanation:

for d) y(0) = 0 and y'(pi) =0

$y(0) = C_1e^0cos(0)+ C_2 e^0 sin(0) = 0 \longrightarrow C_1 = 0$

y(x) ' = C_1e^x cos(x) - C_1e^x sin (x) + C_2e^x sin(x) + C_2e^x cos(x)

$y(\pi)'=C_1e^\pi cos(\pi)- C_1e^\pi sin(\pi)+ C_2e^\pi sin(\pi) + C_2e^\pi cos (\pi)$

Replace C_1 = 0 we have

$y'(\pi) = -C_2e^\pi = 0$

if and only if C_2 =0

Hence the given solution does not work.

then, d is NOT the correct answer.

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imhereforas

08.07.2022

Put a pic and I’ll help you, until then That doesn’t make sense and can’t be solved on its own

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