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mathi85
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Task 7
Show that y=(1/4)tsin2t satisfies equation
d2y/dt2+4y=cos2t
Find the general solution and deduce the solution which satisfies y(0)=0 and y'(0)=0. What happens as t increases?
Solution
In the end I stay with:
y=Acos2t+Bsin2t+(1/4)tsin2t
dy/dx=-2Asin2t+2Bcos2t+(1/2)tcos2t+(1/4)sin2t
After applying boundary conditions I get:
0=0
What does it mean and what happens as 't' is increasing? I was asked to plot a graph.
Show that y=(1/4)tsin2t satisfies equation
d2y/dt2+4y=cos2t
Find the general solution and deduce the solution which satisfies y(0)=0 and y'(0)=0. What happens as t increases?
Solution
In the end I stay with:
y=Acos2t+Bsin2t+(1/4)tsin2t
dy/dx=-2Asin2t+2Bcos2t+(1/2)tcos2t+(1/4)sin2t
After applying boundary conditions I get:
0=0
What does it mean and what happens as 't' is increasing? I was asked to plot a graph.