Q7 of 68 Page 902

Verify that y = ae^2x + be ^{- x} is the general solution of the differential equation

Given

On differentiating with x, we get

On differentiating again with x, we get

Now let’s see what is the value of

= 0

Conclusion : Therefore, is the solution of

Verify that y = A cos 2x - B sin 2x is the general solution of the differential equation = 0.

Verify that y = ae^2x + be ^{- x} is the general solution of the differential equation

Show that y = e^x(A cos x + B sin x) is the solution of the differential equation

Questions · 68

18. Differential Equations and Their Formation

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Verify that y = ae2x + be - x is the general solution of the differential equation