Transform the given differential equation or system into an equivalent system of first-order differential equations.x ^ { \prime \prime } + 3 x' - 7x

shadsiei

shadsiei

Answered question

2021-05-05

Transform the given differential equation or system into an equivalent system of first-order differential equations.
x+3x7x=t2

Answer & Explanation

StrycharzT

StrycharzT

Skilled2021-05-06Added 102 answers

The second-order equation
x+3x+7x=t2
is equivalent to equation
f(t,x,x)=t27x3x
Hence the substitutions x1=x,x2=x=x1 yield the system
x1=x2
x2=t{1}27x13x2

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