How Do You Determine Values of p and q in Differential Equation Superposition?

[Gspace]

Homework Statement

y1[t] solves
y't]+9.7 y[t]=E^(-0.4 t) Cos[t], with y[0]=0,
and y2[t] solves

y'[t]+9.7 y[t]=0, with y[0]=1.

What numbers p and q do you pick to make
y[t]=p y1[t] + q y2[t]
solve
y'[t]+9.7 y[t]=3 E^(-0.4 t) Cos[t], with y[0]=3?

Homework Equations

y1[t] solves
y't]+9.7 y[t]=E^(-0.4 t) Cos[t], with y[0]=0,
and y2[t] solves

y'[t]+9.7 y[t]=0, with y[0]=1.

 

[micromass]

So we got $$y(t)=p y_1(t)+qy_2(t)$$.

What you need to do now is to plug this y(t) in you equation $$y^\prime(t)+9,7y(t)=3e^{- 0,4 t}$$. You will obtain a nice equation this way which you need to solve...

 

[Gspace]

Makes sense. Thanks micromass