Solve \((1+{ 2e }^{ x/y })dx+2{ e }^{ x/y }\left( 1-\frac { x }{ y } \right) dy=0\)

Solve the following differential equations
(x³+ y³) dy-x²ydx = 0

Solve the Linear differential equation:
\(\frac { dy }{ dx } +\frac { y }{ x } =sinx\)

The growth of a population is proportional to the number present. If the population of a colony doubles in 50 years, in how many years will the population become triple?

A pot of boiling water at 100^o C is removed from a stove at time t = 0 and left to cool in the kitchen. After 5 minutes, the water temperature has decreased to 80^o C , and another 5 minutes later it has dropped to 65^oC. Determine the temperature of the kitchen.