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Form the differential equation not conta...

Form the differential equation not containing the arbitrary constants and satisfied by the equation `y=a e^(b x),`a` and `b` are arbitrary constants.

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To form the differential equation that does not contain the arbitrary constants \( a \) and \( b \) and is satisfied by the equation \( y = a e^{bx} \), we will follow these steps: ### Step 1: Differentiate the given function Given: \[ y = a e^{bx} \] We differentiate \( y \) with respect to \( x \): ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Find the equation of a curve passing through the point (0, 1). If t...

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  2. Form the differential equation corresponding to y^2=m(a^2-x^2) by eli...

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  3. Form the differential equation not containing the arbitrary constant...

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  4. if (log)a x=b for permissible values of a and x then identify the stat...

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  5. Form the differential equation corresponding to y^2=a(b-x)(b+x) by eli...

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  6. In each of the following differential equations indicate its degree...

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  7. Form the differential equation of the family of curves represented ...

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  8. Determine the order and degree of each of the following differentia...

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  9. Show that the differential equation that represents the family of al...

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  10. Find the differential equation of All non-vertical lines in a plane.

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  11. Solve the following differential equations: (dy)/(dx)=ytanx-2sinx

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  12. Solve the following differential equations: (dy)/(dx)+y cotx=x^2cotx+2...

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  13. Solve the following differential equations: (dy)/(dx)+(4x)/(x^2+1)y+1/...

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  14. Solve the following differential equations: x(dy)/(dx)-y=(x-1)e^x

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  15. Solve each of the following initial value problems sqrt(1-y^2)dx=...

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  16. Solve the following differential equations: x(dy)/(dx)+y=x e^x

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  17. If y(t) is a solution of (1+t)(dy)/(dt)-t y=1a n dy(0)=-1 then show ...

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  18. Solve: (x+2y^3)dy=ydxdot

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  19. Solve each of the following initial value problems: x(dy)/(dx...

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  20. Solve each of the following initial value problems: (dy)/(dx)+(2x)/(...

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