Q. 243.7( 3 Votes )

Solve , y(1) = - 1.

Answer :

Given, A differential equation

To find: Find the solution of the differential equation , for y(1) = - 1


Explanation: We have given a differential equation


We can write it as ,



Now, integrating both sides,





Here, we know, and


For y, and


So,


…(i)


Now, y(1) = - 1 , then


Put x = 1 and y = - 1 in equation (i)



- 1 - 2 log 1 = 1 + 2 log 1 + C


- 1 = 1 + C


C = - 2


On putting C = - 2 in equation (i), we get



Since, mlog n = log nm


y - x + 2 = log (y + 2)2 + log x2


Since, log m + log n = log mn


y - x + 2 = log (x2(y + 2)2)


Hence, The solution of the given differential equation is


y - x + 2 = log(x2(y + 2)2)


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