1. find a general solution of the equation by" + boy! + 180y = 250xe - x 2 . Assume we have a first order differential equation written in the form N ( x , Y ) d x - M ( x , y ) dy = 0 A. when is the equation exact ? B. It the equation is not exact , what is the integrating tactor F ( x, y ) for this equation? C IS the equation exact if N ( X,y ) = 5 + x and M ( X, V ) = 5? 3. Consider an equation x2y' - 2xBy = x4 ex2 A . find the general solution of the equation B find a solution of the initial value problem with y (1 ) = 1/ 2 4 . We have two functions YI = XII and 12 = x2 / 2+ x A. Calculate Wronskian W(x) of those functions? B. Are these functions linearly independent in the interval OLX4/ 5. Solve the equation yyll = 3 (y ' ) 2 6. Reduce the ODE y 'll + 2 ( y ' ) 2 - exp ( - x ) y = o to a function system of ODES 7. Consider the function + ( x,y ) = cos ( 4 1 x ) A . IS this a homogeneous function ? why ? B. It yes, what is the degree of this function