ODE
\[ y'''(x)=x y(x) \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0367222 (sec), leaf count = 78
\[\left \{\left \{y(x)\to \frac {1}{8} \left (8 c_1 \, _0F_2\left (;\frac {1}{2},\frac {3}{4};\frac {x^4}{64}\right )+x \left ((2+2 i) c_2 \, _0F_2\left (;\frac {3}{4},\frac {5}{4};\frac {x^4}{64}\right )+i c_3 x \, _0F_2\left (;\frac {5}{4},\frac {3}{2};\frac {x^4}{64}\right )\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.159 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {1}{2}},{\frac {3}{4}};\,{\frac {{x}^{4}}{64}})}+{\it \_C2}\,x{\mbox {$_0$F$_2$}(\ ;\,{\frac {3}{4}},{\frac {5}{4}};\,{\frac {{x}^{4}}{64}})}+{\it \_C3}\,{x}^{2}{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{4}},{\frac {3}{2}};\,{\frac {{x}^{4}}{64}})} \right \} \] Mathematica raw input
DSolve[y'''[x] == x*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (8*C[1]*HypergeometricPFQ[{}, {1/2, 3/4}, x^4/64] + x*((2 + 2*I)*C[2]*HypergeometricPFQ[{}, {3/4, 5/4}, x^4/64] + I*x*C[3]*HypergeometricPFQ[{}, {5/4, 3/2}, x^4/64]))/8}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = x*y(x), y(x),'implicit')
Maple raw output
y(x) = _C1*hypergeom([],[1/2, 3/4],1/64*x^4)+_C2*x*hypergeom([],[3/4, 5/4],1/64*x^4)+_C3*x^2*hypergeom([],[5/4, 3/2],1/64*x^4)