first order ode

Pick the CORRECT solution for the following differential equation $\frac{d y}{d x}=e^{x-y}$

Consider the following differential equation $$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$ $$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left...

A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^ \circ }$$c. What will be the temperature of the body at the...

The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is

Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ i...

If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is