Solve the differential equation.

left parenthesis t minus $1$ right parenthesis cubed s prime plus $4$ left parenthesis t minus $1$ right parenthesis squared s equals t plus $1($t$1)3$s$+4($t$1)2$s$=$t$+1,$

t greater than $1$t$>1$

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Part $1$

The solution is

sequals$=$enter your response here.