1. Solve the initial value problem xy² dy/dx = y3+x3 with y(1)= 2 2. Solve the following Bernoulli differential equation dy/dx - y = y²ex 3. Solve the differential equation (check if its homogenous). dy/dx = y(x-y)/x² 4. Solve the (separable) differential equation. dy/dx = y(y + 2) 5. Solve the following linear differential equation. x dy/dx = y+2x3 6. Solve the following differential equation (check if it exact). 2xy -9x2+ (2y+x²+1) dy/dx= 0