Q14 of 26 Page 1

Solve the differential equation :

Given:


Re - writing the given equation as



Assuming and differentiating both sides






Now integrating both sides,



Formula:




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12

Evaluate :

OR


Evaluate:

13

Solve the differential equation :

 15

Ishan wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by Using matrices, find the dimensions of the plot. Also, give a reason why he wants to donate the plot for a school.

 16

Prove that

OR


Solve the equation for x :