Find the ODE that satisfies the solution yx 5 cos4x 5sin4x

Find the ODE that satisfies the solution: y(x) = 5 cos(4x) + 5sin(4x) In the form Ay\" + By\' + Cy = 0

Let us substitute and see what we get

-80A cos(4x)-80A sin(4x) -20B sin(4x)+20B cos(4x) +5C cos(4x)+5C sin(4x)=0

-80A+20B+5C=0

-80A-20B+5C=0

Hence,B=0

C=16A

SO the ode is

Ay\'\'+16Ay=0

$Find the ODE that satisfies the solution: y(x) = 5 cos(4x) + 5sin(4x) In the form Ay\$