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Consider the differential equation: $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left( {1 + {{\text{y}}^2}} \right){\text{x}}{\text{.}}$$
The general solution with constant c is

Consider the differential equation: $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left( {1 + {{\text{y}}^2}} \right){\text{x}}{\text{.}}$$
The general solution with constant c is Correct Answer $${\text{y}} = \tan \left( {\frac{{{{\text{x}}^2}}}{2} + {\text{c}}} \right)$$

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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?
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