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Find the differential equation of the ci...

Find the differential equation of the circles represented by `y = k(x + k)^(2)` where k is an arbitrary constant.

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To find the differential equation of the circles represented by the equation \( y = k(x + k)^2 \), where \( k \) is an arbitrary constant, we can follow these steps: ### Step 1: Differentiate the given equation We start with the equation: \[ y = k(x + k)^2 \] To eliminate the constant \( k \), we differentiate both sides with respect to \( x \): ...
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AAKASH INSTITUTE ENGLISH-DIFFERENTIAL EQUATIONS-Try Yourself
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  9. Find the equation of the curve passing through origin and satisfying t...

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  10. Solve the differential equation x sec^(2) y dy = (xIn x + 1) e^(x) dx.

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  12. Show that the differential equation x^(2)(dy)/(dx) = x^(2)+ xy + y^(2)...

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  13. Show that (3xy + x^(2)) dy + (y^(2) + xy)dx = 0 is homogeneous differe...

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  14. Find the general solution of the equation x - y (dx)/(dy) = y + x (dx)...

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  15. Solve the following differential equation : ( 1 + e^(y/x) ) dy + e...

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  16. Solve the differential equation (dy)/(dx) + 2y = x.

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  17. Find the general solution of the differential equation (x-1)(dy)/(dx) ...

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  18. Solve the differential equation y^(2)(dx)/(dy) + x = 1.

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