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Show that y=a*e^(2x)+b*e^(-x) is a solut...

Show that `y=a*e^(2x)+b*e^(-x)` is a solution of the differential equation `(d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0`.

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To show that \( y = a e^{2x} + b e^{-x} \) is a solution of the differential equation \[ \frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0, \] we will follow these steps: ...
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NAGEEN PRAKASHAN-DIFFERENTIAL EQUATIONS-Miscellaneous Exercise
  1. Show that y=a*e^(2x)+b*e^(-x) is a solution of the differential equati...

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  2. For each of the differential equations given below, indicate its orde...

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  3. For each of the exercises given below, verify that the given function...

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  4. Form the differential equation representing the family of curves give...

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  5. Prove that x^2-y^2=c(x^2+y^2)^2is the general solution of differenti...

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  6. Form the differential equation of the family of circles in the firs...

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  7. Find the general solution of the differential equation (dy)/(dx)+sqrt...

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  8. Show that the general solution of the differentia equation (dy)/(dx)...

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  9. Find the equation of the curve passing through the point (0,pi/4) w...

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  10. Find the particular solution of the differential equation: (1+e^(2x))d...

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  11. Solve the differential equation y e^(x/y)dx=(x e^(x/y)+y^2)dy(y!=0)

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  12. Find a particular solution of the differential equation(x" "" "y)" ...

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  13. Solve the differential equation [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x)...

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  14. Find the particular solution of the differential equation. (dy)/(dx...

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  15. find the particular solution satisfying the given condition, for the f...

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  16. The population of a village increases continuously at the rate prop...

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  17. The general solution of the differential equation (ydx-xdy)/(y)=0 is :

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  18. The general solution of a differential equation of the type (dx)/(d...

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  19. The solution of the differential equation, e^x(x +1)dx + (ye^y -xe^x)d...

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