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Verify that y=4sin3x is a solution of th...

Verify that `y=4sin3x` is a solution of the differential equation `(d^2y)/(dx^2)+9y=0.`

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To verify that \( y = 4 \sin(3x) \) is a solution of the differential equation \[ \frac{d^2y}{dx^2} + 9y = 0, \] we will follow these steps: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Verify that the function y=C1e^(a x)cosb x+C2e^(ax)sinb x ,\ C1, C2,\ ...

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  2. Show that y=b e^x+c e^(2x)\ is a solution of the differential equatio...

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  3. Verify that y=4sin3x is a solution of the differential equation (d^2y)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Verify the solution problems: Show that y = e^-x + ax +b is solution o...

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  20. For each of the following differential equations verify that the accom...

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