Final answer:
The general solution of the differential equation x * y' = 6x³ * e⁽²ˣ⁾ * 2y is y = C * e⁽²ˣ⁾ * (x³ + 3x² + 5x + 5), where C is a constant.
Step-by-step explanation:
The given differential equation is x * y' = 6x³ * e⁽²ˣ⁾ * 2y.
To solve this equation, we can separate the variables and integrate both sides.
Dividing both sides by x * 2y, we get dy/dx = 3x² * e⁽²ˣ⁾.
Now, we can integrate both sides to solve for y.
After solving the integrals, the general solution of the differential equation is y = C * e⁽²ˣ⁾ * (x³ + 3x² + 5x + 5), where C is a constant.