Q5 of 68 Page 902

Verify that y = e^x(A cos x + B sin 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 + bx) e^2x is the general solution of the differential equation

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

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

Questions · 68

18. Differential Equations and Their Formation

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