Solve : \({ e }^{ \frac { dy }{ dx } }=x+1,y(0)=5\)

Solve : \(\left( 1+{ x }^{ 2 } \right) \frac { dy }{ dx } -x={ 2tan }^{ -1 }x\)

Solve : \(\left( { x }^{ 2 }+{ x }^{ 2 }+x+1 \right) \frac { dy }{ dx } ={ 2x }^{ 2 }+x\)

Solve : (1+y²)(1 + log x)dx + x dy = 0, given that x = 1,y = 1.

In a bank principal increases at the rate of 5% per year. In how many years Rs.1000 doubled itself.

Sovle : (x+y+1)²dy=dx,y(-1)=0

Solve :x²dy+y(x+y)dx=0 given that y=1 when x=1.

Solve :(x²+xy)dy=(x²+y²)dx

Solve :\(x\frac { dy }{ dx } sin\left( \frac { y }{ x } \right) +x-ysin\left( y\frac { y }{ x } \right) =,y(1)=\frac { \pi }{ 2 } \)

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

Solve : \({ cos }^{ 2 }x\frac { dy }{ dx } +y=tanx(0\le x\le \frac { \pi }{ 2 } )\)

Solve : \(\frac { dy }{ dx } =-\frac { x+ycos }{ 1+sinx } \) .Also find the domain of the function.

Solve : (x-siny)dy+tanydx=0,y(0)=0

It is given that the rate at which some bacteria multiply is proportional to the instantaneous number present. If the original number of bacteria doubles in two hours, in how many hours will it be five times.

Water at temperature 100℃ cools in 5 minutes to 80℃ in a room of temperature 30℃. Find (i) the temperature of water after 10 minutes. (ii) the time when the temperature is 40℃.