The type of the partial differential equation $${{\partial f} \over {\partial t}} = {{{\partial ^2}f} \over {\partial {x^2}}}\,\,is$$

While numerically solving the differential equation $$\,{{dy} \over {dx}} + 2x{y^2} = 0,y\left( 0 \right) = 1\,\,$$ using Euler's predictor corrector (improved Euler- Cauchy) method with a step size of $$0.2,$$ the value of $$y$$ after the first step is