2.1451   ODE No. 1451

\[ y^{(3)}(x)-a x^b y(x)=0 \]

✓ Mathematica : cpu = 0.0183629 (sec), leaf count = 168

DSolve[-(a*x^b*y[x]) + Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to (-1)^{\frac {1}{b+3}} (b+3)^{-\frac {3}{b+3}} c_2 x a^{\frac {1}{b+3}} \, _0F_2\left (;1-\frac {1}{b+3},1+\frac {1}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )+(-1)^{\frac {2}{b+3}} (b+3)^{-\frac {6}{b+3}} c_3 x^2 a^{\frac {2}{b+3}} \, _0F_2\left (;1+\frac {1}{b+3},1+\frac {2}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )+c_1 \, _0F_2\left (;1-\frac {2}{b+3},1-\frac {1}{b+3};\frac {a x^{b+3}}{(b+3)^3}\right )\right \}\right \}\]

✓ Maple : cpu = 0.166 (sec), leaf count = 114

dsolve(diff(diff(diff(y(x),x),x),x)-a*x^b*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {1+b}{b +3}, \frac {b +2}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )+c_{2} x \operatorname {hypergeom}\left (\left [\right ], \left [\frac {b +4}{b +3}, \frac {b +2}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )+c_{3} x^{2} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {b +5}{b +3}, \frac {b +4}{b +3}\right ], \frac {a \,x^{b +3}}{\left (b +3\right )^{3}}\right )\]