Pregunta: Determine in each problem whether or not the following function is a solution of the given differential equation, where C is a constant: i. y′=−2x2y+ex;y=2xC−ex ii. y′+y=1;y=1+Ce−x iii. 2yy′=1;y=x−1 iv. x2yy′=−1−xy2;y=2x4−x2 v. y′+y=0;y=Ce−x vi. y′=2−x22xy;y=x2−2C vii. xy′=−y+x;y=2xx2−3

please solve i. and vi.