11. Solve yyp + 2px, where p = dy/dx 5 12. Solve (D2-3D+2)y = x+x 5 13. Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference of temperature between the object and its surroundings. Supposing water at 100C cools to 80C in 10 minutes, in a room temperature of 30C, find when the temperature of water will become 40C? OR Solve the differential equation x dy dx2 X + y = logx. dy dx 14. Find the condition that the line lx +my+n=0 may be the tangent to the ellipse 15. Derive the equation of a hyperbola in standard form. 5 x 2 y2 + a b2 16. Find the centre, length of axes and eccentricity of the conic 2x +3y-4x-12y+ 13 = 0. OR 10 Identify and sketch the conic r = 3+2 cos 0 S - 1.