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Verify that the function y=C1e^(a x)cosb...

Verify that the function `y=C_1e^(a x)cosb x+C_2e^(ax)sinb x ,\ C_1, C_2,\ ` are arbitrary constants is a solution of the differential equation `(d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0`

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To verify that the function \[ y = C_1 e^{ax} \cos(bx) + C_2 e^{ax} \sin(bx) \] is a solution of the differential equation ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
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  3. Verify that the function y=C1e^(a x)cosb x+C2e^(ax)sinb x ,\ C1, C2,\ ...

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  6. Show that y=a e^(2x)+b e^(-x) is a solution of the differential equa...

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  7. Show that the function y=A cos x+B sin x\ is as solution of the diffe...

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  8. Show that the function y=A cos\ 2x-B sin\ 2x\ is a solution of the di...

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  9. Show that\ y=A e^(B x) is as solution of the differential equation (d^...

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  10. Verity that y=a/x+b is a solution of the differential equation (d^2y)/...

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  11. Verify that y^2=4a x is a solution of the differential equation y=x(dy...

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  12. Show that A x^2+B y^2=1 is a solution of the differential equation x{y...

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  13. Show that y=a x^3+b x^2+c is a solution of the differential equation (...

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  14. Show that y=(c-x)/(1+c x) is a solution of the different equation (1+x...

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  15. Show that y=e^x(A\ cos x+Bsinx) is the solution of the differential eq...

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  16. Verify that y=c x+2c^2 is a solution of the differential equation 2((d...

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  17. Verify that y=-x-1 is a solution of the differential equation (y...

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  18. Verity that y^2=4a\ (x+a) is a solution of the differential equatio...

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  19. Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x...

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  20. Show that the differential equation of which y=2(x^2-1)+c e^-x^2 is a ...

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