Question

how do we solve the initial-value problem?

−7y''−7y=sin(x); y(0)=2y(0)=−4

Answer 1

for the homogenous solution, use -7(r^2+1)=0 or r^2= -1
This gives exp(-ix) and exp(ix), or Asin(x) + Bcos(x), A and B to be determined.
for the particular, assume yp= x(Csin(x) + Dcos(x))
we multiply by x to be orthogonal to the homogenous solution.
sub yp into the equation, simplify and match coeffs.
not sure what the initial conditions are. y(0)= 2 ? y'(0)= -4?

Answer 2

yea they are

Answer 3

omar sorry it isnt right

Answer 4

and phi could you please show me a step my step solution?

Answer 5

:$