\[ (-20 x-30) \left (x^2+3 x\right )^{7/3}+x (x+3) y''(x)+(3 x-1) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 10.437 (sec), leaf count = 179
DSolve[(-30 - 20*x)*(3*x + x^2)^(7/3) + y[x] + (-1 + 3*x)*Derivative[1][y][x] + x*(3 + x)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 \left (-4 \sqrt {3} x^{4/3} \arctan \left (\frac {\sqrt {3} \sqrt [3]{x}}{\sqrt [3]{x}+2 \sqrt [3]{x+3}}\right )-4 x^{4/3} \log \left (\sqrt [3]{x+3}-\sqrt [3]{x}\right )+2 x^{4/3} \log \left (x^{2/3}+\sqrt [3]{x+3} \sqrt [3]{x}+(x+3)^{2/3}\right )-15 \sqrt [3]{x+3} x-9 \sqrt [3]{x+3}\right )}{4 (x+3)^{7/3}}+\frac {c_1 x^{4/3}}{(x+3)^{7/3}}+\frac {9}{340} \sqrt [3]{x (x+3)} \left (17 x^2-9 x\right ) (x+3)^3\right \}\right \}\] ✓ Maple : cpu = 0.092 (sec), leaf count = 52
dsolve(x*(x+3)*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)+y(x)-(20*x+30)*(x^2+3*x)^(7/3)=0,y(x))
\[y \left (x \right ) = \frac {\left (c_{2}+\int \frac {\left (c_{1}+3 \left (x^{2}+3 x \right )^{\frac {7}{3}} x \left (x +3\right )\right ) \left (x +3\right )^{\frac {7}{3}}}{x^{\frac {4}{3}} \left (x^{2}+3 x \right )}d x \right ) x^{\frac {4}{3}}}{\left (x +3\right )^{\frac {7}{3}}}\]