2.1263   ODE No. 1263

\[ (-20 x-30) \left (x^2+3 x\right )^{7/3}+x (x+3) y''(x)+(3 x-1) y'(x)+y(x)=0 \]

✓ Mathematica : cpu = 0.683353 (sec), leaf count = 349

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]
 

\[\left \{\left \{y(x)\to \frac {c_1 x^{4/3}}{(x+3)^{7/3}}+\frac {c_2 \left (-15 x^{4/3}-4 \sqrt [3]{\frac {x}{x+3}} x^{4/3} \log \left (\sqrt [3]{x+3}-\sqrt [3]{x}\right )+2 \sqrt [3]{\frac {x}{x+3}} x^{4/3} \log \left (x^{2/3}+\sqrt [3]{x+3} \sqrt [3]{x}+(x+3)^{2/3}\right )-4 \sqrt {3} \sqrt [3]{\frac {x}{x+3}} x^{4/3} \tan ^{-1}\left (\frac {\sqrt {3} \sqrt [3]{x}}{\sqrt [3]{x}+2 \sqrt [3]{x+3}}\right )-9 \sqrt [3]{\frac {x}{x+3}} \sqrt [3]{x+3}\right )}{4 \sqrt [3]{\frac {x}{x+3}} (x+3)^{7/3}}+\frac {9 \left (5775 x^{13/3}-7425 x^{10/3}+6075 x^{7/3}+1309 \sqrt [3]{\frac {x}{x+3}} \sqrt [3]{x+3} x^5+1386 \sqrt [3]{\frac {x}{x+3}} \sqrt [3]{x+3} x^4+15048 \sqrt [3]{\frac {x}{x+3}} \sqrt [3]{x+3} x^3-12312 \sqrt [3]{\frac {x}{x+3}} \sqrt [3]{x+3} x^2\right ) (x+3)^{5/3}}{26180 \sqrt [3]{\frac {x}{x+3}} (x (x+3))^{2/3}}\right \}\right \}\]

✓ Maple : cpu = 0.116 (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))
 

\[y \left (x \right ) = \frac {\left (c_{2} +\int \frac {\left (c_{1} +3 \left (x^{2}+3 x \right )^{{7}/{3}} x \left (x +3\right )\right ) \left (x +3\right )^{{7}/{3}}}{x^{{4}/{3}} \left (x^{2}+3 x \right )}d x \right ) x^{{4}/{3}}}{\left (x +3\right )^{{7}/{3}}}\]