List of top Mathematics Questions on General and Particular Solutions of a Differential Equation asked in WBJEE

The value of \(\lambda\), such that the following system of equations \(2x - y - 2z = 2\); \(x - 2y + z = -4\); \(x + y + \lambda z = 4\) has no solution, is

The differential equation of the family of curves $y = e^{2x} (a \,\cos\, x + b \,\sin\, x)$, where $a$ and $b$ are arbitrary constants, is given by