Solve  

Solve  

Solve  (x² + y² + x) dx – (2x² + 2y² – y) dy = 0

Solve   

Solve  (x³ + xy² + a²y) dx + (y³ + yx² – a²x) dy = 0

Solve   

Solve  xsiny dy + (x³ – 2cosy + cosy) dx = 0

Solve  dy + (2xtan⁻¹ y – x³) (1 + y²) dx = 0

Solve  x (y² + x² – a²x) dx + y (y² + x² – b²y) dy = 0

If   where A is some constant and v is a function of x which has value 0 when x = 0. Prove that v = 2 e^x sinhx

Solve  dx + (x + 2y) dy = 0

Solve   

Solve   

Solve   

Solve  (y² – 2x²y) dx + (2x³ – xy) dy = 0

Solve  (1 – x²y²) dx = ydx + xdy

Solve   

Solve  (1+ 4xy + 2y²) dx + (1 + 4xy + 2x²) dy = 0

Solve   

If the population of a country doubles in 50 years, in how many years will it triple under the assumption that the rate of increase is proportional to the number of inhabitants?

In a certain culture of bacteria the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, how many may be expected at the end of 12 hours.

According to Newton’s law of cooling the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of air. If the temperature of air is 30° and the substance cools from 100° to 70° in 15 minutes, find when the temperature will be 40°.

If yʹ = y + 1 and y (0) = 1 then value of y (ln2) is