(3x-1)y'=6y-10(3x-1)^1/3
You asked:
Investigate the equation: \(\left(3 x - 1\right) \cdot y^{\prime} = 6 y - \frac{10 \cdot {\left( 3 x - 1 \right)}^{1}}{3}\).
MathBot Answer:
\[y{\left(x \right)} = - \frac{10}{9} + \frac{10 x}{3} - 6 C_{1} x + 9 x^{2} C_{1} + C_{1}\]
\(C_{1}\) is an arbitrary constant.