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Question

drdt=-rt, r0=r0

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Solution

We have,drdt=-rt, r0=r0

1rdr =-t dtIntegrating both sides, we get1rdr =-t dtlog r=-t22+C ....(1)Given: t=0, r=r0. Substituting the values of x and y in (1), we getlog r0 =0+CC=log r0 Substituting the value of C in (1), we get
log r=-t22+log r0 log r -log r0 =-t22log rr0=-t22r=r0e-t22Hence, r=r0e-t22 is the required solution.

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