Solve: (x+y)²\(\frac { dy }{ dx } \) = 1

Find the equation of the curve passing through (1, 0) and which has slope 1+ \(\frac { y }{ x } \) at (x, y).

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^x-x-1).

Solve: (D²+1)y = 0 when x = 0, y = 2 and when x = \(\frac { \pi }{ 2 } \), y = -2.

A man plans to invest some amount in a small saving scheme with a guaranteed compound in crest compounded continuously at the ratio of 12 percent for 5 years. How much should he invest if he wants an amount of Rs. 25000 at the end of 5 year period? (e^-0.6 = 0.5488)