Solving Very Hard Integral g(x) - Joe

[A_I_]

g(x) is a function of x that we do not know its form.


y(t) =(1/2) integral 0-->t [ sin(2t-2x)*g(x) ]dx

i tried to use integration by substitution and by parts
but the problem is that g(x) has an unknown form.

the actual problem is that

y" +cy' +dy = g(t) y(0) = y0 y'(0) = y'0

we are asked to find c,d,y0,y'0
knowing that y(t) is the solution of the second order differential equation.

i would appreciate your help.
Thanks,
Joe

 

[arildno]

Evaluate y(0) to find y0.

Differentiate y and evaluate y'(0) to find y'0

Insert y' and y'' in your equation, and determine c and d from that.

Remember Leibniz' rule for differentiating an integral with variable limits!