Q8 of 68 Page 902

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

Verify that y^{2 =} 4a(x + a) is a solution of the differential equation

Questions · 68

18. Differential Equations and Their Formation

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