Solve \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -\frac { 3dx }{ dt } +2x\) = 0 given that when t = 0, x = 0 and \(\frac { dx }{ dt } \) = 1

Solve the following differential equations: (4D²+4D−3)y = e^2x

Form the differential equation having for its general solution y = ax² + bx

Solve x \(\frac{dy}{dx}\) + 2y = x⁴

Find the order and degree of the following differential equations.
\(\frac{d^{3} y}{d x^{3}}+3\left(\frac{d y}{d x}\right)^{3}+2 \frac{d y}{d x}=0\)