The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is

The type of partial differential equation $${{{\partial ^2}p} \over {\partial {x^2}}} + {{{\partial ^2}p} \over {\partial {y^2}}} + 3{{{\partial ^2}p} \over {\partial x\partial y}} + 2{{\partial p} \over {\partial x}} - {{\partial p} \over {\partial y}} = 0$$ is

The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is

The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is