Problem:
Consider the differential equation
y‴+y′y+y2=cos(t)
which is the correct conversion of this equation into first-order form
Consider also the boundary conditions
y′′(0)=5,y(0)=3,y(1)y′(1)+y(1)=0
What is the correct implementation of these boundary conditions in the first-order system.
Solution:
Let y1=y, y2=y′, y3=y″, we have
y′1=y2
y′2=y3
y′3=y‴=cos(t)−y′y−y2=cos(t)−y1y2−y21
y″(0)=5⟹y3(0)=5
y(0)=3⟹y1(0)=3
y(1)y′(1)+y(1)=0⟹y1(1)y2(1)+y1(1)=0
Consider the differential equation
y‴+y′y+y2=cos(t)
which is the correct conversion of this equation into first-order form
Consider also the boundary conditions
y′′(0)=5,y(0)=3,y(1)y′(1)+y(1)=0
What is the correct implementation of these boundary conditions in the first-order system.
Solution:
Let y1=y, y2=y′, y3=y″, we have
y′1=y2
y′2=y3
y′3=y‴=cos(t)−y′y−y2=cos(t)−y1y2−y21
y″(0)=5⟹y3(0)=5
y(0)=3⟹y1(0)=3
y(1)y′(1)+y(1)=0⟹y1(1)y2(1)+y1(1)=0
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