Question

The given two-parameter family is a solution of the indicated differential equation on the interval

Answer 1

Answer:

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.