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Reduce the differential equation (d^2y)/...

Reduce the differential equation `(d^2y)/dx^2-2 dy/dx+y=xe^x` using the transformation `y=v(x).e^x`. Hence solve the equation when `y=1, dy/dx=0`, for `x=0`

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A DAS GUPTA-Differential Equation of the First Order-Exercise
  1. Obtain all the solutions of (y+1)(dy/dx)+2=x(dy/dx)^2

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  2. solve the differential equationx(d^2y)/dx^2+dy/dx=0.

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  3. Reduce the differential equation (d^2y)/dx^2-2 dy/dx+y=xe^x using the ...

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  4. A radioactive substance is subject to the law of natural decay (dv)/(d...

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  5. A country has a food deficit of 10%. Its population grows continuously...

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  6. Show that the equation of the curve passing through the point (1,0) an...

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  7. Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x an...

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  8. Find the equation of the curve such that the square of the intercept c...

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  9. Find the curves for which the length of normal is equal to the radius ...

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  10. Find the cartesian equation of the curves for which the length of the ...

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  11. Find the equation of the curve for which the length of the normal is c...

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  12. Find the equation of the curve which is such that the area of the rect...

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  13. The equation of the curve in which the portion of the tangent included...

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  14. The equation of the curve such that the distance between the origin a...

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  15. The normal PG to a curve meets the x-axis in G. If the distance of G f...

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  16. Find the equation of curves for which the cartesian subtangent varies ...

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  17. Find the equation of the curve in which the subnormal varies as the ...

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  18. Find the orthogonal trajectory of y^2=4a x (a being the parameter).

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  19. Prove that the family of curves x^2/(a^2+lambda)+y^2/(b^2+lambda)=1, w...

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  20. For the differential equation sqrt(1+(d^2y)/(dx^2))=x, the degree=and ...

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