Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. `y = e^x (a cos x + b sin x)`

Explanation

`y=e^x (A cosx+B sinx)`

`y^1 =e^x (−A sinx+B
cosx)+e^x (A cosx+B sinx)`

`y^1
=e^x(A(cosx−sinx)+B(cosx+sinx))`

`y^2 =e^x(A(−sinx−cosx)+B(sinx+cosx))+e^x(A(cosx−sinx)+B(cosx+sinx))

y^2` =`e^x(A(−2sinx))+B(2cosx))`

`y^2 =2e^x(Bcosx−Asinx)`

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