 Good morning friends, I am Poorwa and today I will help you with the following question which of the following differential equations has y is equal to c1 into e raised to the power x plus c2 into e raised to the power minus x as the general solution a d square y by dx square plus y is equal to 0 b d square y by dx square minus y is equal to 0 c d square y by dx square plus 1 is equal to 0 d d square y by dx square minus 1 is equal to 0 Let us now begin with this solution So here we are given that y is equal to c1 into e raised to the power x plus c2 into e raised to the power minus x and Let us mark this as equation 1 Now we shall form a differential equation whose solution is equation 1 by Differentiating it two times as it contains two arbitrary constants c1 and c2 So differentiating one with respect to x we get differentiating y gives dy by dx is equal to differentiating c1 into e raised to the power x gives c1 into e raised to the power x and differentiating c2 into e raised to the power minus x gives minus c2 into e raised to the power minus x and let us mark this as equation 2 Now we differentiate equation 2 with respect to x so differentiating 2 with respect to x we get differentiating dy by dx we get d square y by dx square is equal to differentiating c1 into e raised to the power x we get c1 into e raised to the power x minus differentiating c2 into e raised to the power minus x we get minus c2 into e raised to the power minus x We can write this as this implies d square y by dx square is Equal to c1 into e raised to the power x now minus into minus will become plus so plus c2 into e raised to the power minus x this implies d square y by dx square is Equal to now by equation 1 we have y is equal to c1 into e raised to the power x plus c2 into e raised to the power minus x so we get d square y by dx square is equal to y and this is by equation 1 and this implies d square y by dx square minus y is equal to 0 and this is same as equation b so we get hence equation b is the required differential equation Thus, we write our answer as b. Hope you have understood the solution. Bye and take care