(8x³y-12x³)dx+(x⁴+1)dy=0
1. Is the given differential equation exact, separable, linear, or homogeneous?
2. Solve the initial value problem: (e(2x)y²-2x)dx+e(2x)ydy=0, y(0)=2
3. Find the solution to the differential equation: (dy)/(dx)=(4x³y²-3x²y)/(x³-2x⁴y)
4. Classify the differential equation: (dy)/(dx)=(2x²+y²)/(2xy-x²)