find the solution yx of the initial value problem fracd yd xx1 y2 quad

Question

) Find the solution y(x) of the initial value problem \frac{d y}{d x}=(x+1) y^{2}, \quad y(0)=2 O The current i(t) flowing through an RL-circuit resulting from the application of a sinu-soidal voltage may be modelled by the initial value problem \frac{d i}{d t}+2 i=\cos (t), \quad i(0)=0 Solve the differential equation for the current i(t) and identify the natural and forced response of the RL-circuit.(11 marks)