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