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

Solve  (a² – 2xy – y²) dx = (x + y)² dy

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?

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