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In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.
What is the order of the differential equation whose solution is y = a cos x + b sin x + ce-x + d, where a, b, c and d are arbitrary constants?
A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained?
The solution of an ODE contains arbitrary constants, the solution to a PDE contains arbitrary functions.
The numbers of arbitrary constants in the particular solution of a differential equation of third order are:
What is the number of arbitrary constants in the particular solution of differential equation of third order?
How many arbitrary constants will be there in the general solution of a second order differential equation?
The number of arbitrary constants in a particular solution of a fourth order differential equation is __________________
A chemical solution appears green when the salt concentration is 8 grams per litre (gpl) and red when it is 10 gpl. Pure water was added to the solution of 1 litre of 15 gpl solution till it turned green. Then 125 ml of the green solution is taken out and x grams of salt is added to the green solution to make it red. Another 500 ml of the final solution was taken out and y litres of green solution is added to get a resultant solution of concentration 9.6 gpl.  Assume adding salt doesn’t change its volume and find the ratio of x and y. 
A differential equation is given as
$${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} - 2{\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{y}} = 4$$
The solution of differential equation in terms of arbitrary constant C1 and C2 is