integrating-factor

Consider the differential equation given below. $${{dy} \over {dx}} + {x \over {1 - {x^2}}}y = x\sqrt y $$ The integrating factor of the differential equation is

Consider the differential equation $$\,\,{{dx} \over {dt}} = 10 - 0.2\,x$$ with initial condition $$x(0)=1.$$ The response $$x(t)$$ for $$t > 0$$ is

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is