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The solution of an ODE contains arbitrary constants, the solution to a PDE contains arbitrary functions.
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?
Which of the following statement(s) is/are correct, regarding the duties and rights of the Attorney-General for India in performance of his duties?
1. The Attorney-General for India shall give advice to the Government of India upon legal matters.
2. The Attorney-General for India shall have a right to audience in all Courts in India.
3. The Attorney-General for India shall have the right to speak in the proceedings of either House.
4. The Attorney-General for India shall not be liable to any proceedings in any court in respect of anything said by him in Parliament or any committee thereof.
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.
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. 
How many arbitrary constants will be there in the general solution of a second order differential equation?
The general solution of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 2\frac{{{\text{dy}}}}{{{\text{dx}}}} - 5{\text{y}} = 0$$     in terms of arbitrary constants K1 and K2 is
Consider the following with reference to Article 18? (a) No title, not being a military or academic distinction, shall be conferred by the State. (b) The citizen of India shall accept any title from any foreign State. (c) No person who is not a citizen of India shall, while he holds any office of profit or trust under the State, accept without the consent of the President any title from any foreign State. (d) The person holding any office of profit or trust under the State shall, without the consent of the President, accept any present, emolument, or office of any kind from or under any foreign State.
What is the general form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)?
A particular solution for an equation is derived by substituting particular values to the arbitrary constants in the complete solution.