Transform the given differential equation or system into an equivalent system of

Cem Hayes

Cem Hayes

Answered question

2021-09-16

Transform the given differential equation or system into an equivalent system of first-order differential equations.
x+3x+7x=t2

Answer & Explanation

Anonym

Anonym

Skilled2021-09-17Added 108 answers

Step 1
Given:
x+3x+7x=t2
Step 2
Substituting y1=x,y2=x, we get
y1=x=y2,y2=(x)=x
But from the original differential equation x+3x+7x=t2, we have
x+3x+7x=t2
x=t23x7x
Substituting x=y1,x=y2 we get
y2=t23y27y1
Therefore, our original differential equation is equivalent to
y1=x=y2,
y2=x=t23y27y1
Therefore, we have the following system, of linear first order differential equations
y1=y2
y2=7y13y2+t2

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