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Verify that the function y=e^(-3x)is a s...

Verify that the function `y=e^(-3x)`is a solution of the differential equation `(d^2y)/(dx^2)+(dy)/(dx)-6y=0`

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Verified by Experts

`y(x)=e^-3x`
`y'= -3e^-3x`
`y''= 9e^-3x`
putting these value in rhs of the equation:
`9e^-3x-3e^-3x-6e^-3x =0`
so y is the solution
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NCERT-DIFFERENTIAL EQUATIONS-SOLVED EXAMPLES
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  2. Form the differential equation of the family of circles touching the ...

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  3. Form the differential equation representing the family of curves y = ...

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  4. Form the differential equation representing the family of curves y = ...

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  5. Verify that the function y=e^(-3x)is a solution of the differential eq...

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  7. Find the order and degree, if defined, of each of the following differ...

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  8. Form the differential equation representing the family of parabolas h...

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  9. Find the general solution of the differential equation (dy)/(dx)=(x+1...

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  10. Solve the differential equation (tan^(-1)y-x)dy=(1+y^2)dx.

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  11. Verify that the function y=c1e^(a x)cosb x+c2e^(a x)sinb x, where c1...

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  12. Form the differential equation of the family of circles in the second...

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  13. Find the particular solution of the differential equation log ((dy)/(d...

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  14. Solve the differential equation (x dy-y dx)ysin(y/x)=(y dx+x dy)xcos(...

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  15. Find the general solution of the differential equation x(dy)/(dx)+2y=...

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  16. Find the general solution of the differential equation y dx-(x+2y^2)d...

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  17. Find the particular solution of the differential equation (dy)/(dx)+y...

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  18. Find the equation of a curve passing through the point (0, 1). If the...

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  19. Find the particular solution of the differential equation (dy)/(dx)=-...

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  20. Find the general solution of the differential equation (dy)/(dx)=(1+y...

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