4.42.44 \(y'''(x)=x y(x)\)

ODE
\[ y'''(x)=x y(x) \] ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.154114 (sec), leaf count = 76

\[\left \{\left \{y(x)\to c_1 \, _0F_2\left (;\frac {1}{2},\frac {3}{4};\frac {x^4}{64}\right )+\frac {1}{8} x \left ((2+2 i) c_2 \, _0F_2\left (;\frac {3}{4},\frac {5}{4};\frac {x^4}{64}\right )+i c_3 x \, _0F_2\left (;\frac {5}{4},\frac {3}{2};\frac {x^4}{64}\right )\right )\right \}\right \}\]

Maple ✓
cpu = 0.123 (sec), leaf count = 45

\[\left [y \left (x \right ) = \textit {\_C1} \hypergeom \left (\left [\right ], \left [\frac {1}{2}, \frac {3}{4}\right ], \frac {x^{4}}{64}\right )+\textit {\_C2} x \hypergeom \left (\left [\right ], \left [\frac {3}{4}, \frac {5}{4}\right ], \frac {x^{4}}{64}\right )+\textit {\_C3} \,x^{2} \hypergeom \left (\left [\right ], \left [\frac {5}{4}, \frac {3}{2}\right ], \frac {x^{4}}{64}\right )\right ]\] Mathematica raw input

DSolve[y'''[x] == x*y[x],y[x],x]

Mathematica raw output

{{y[x] -> C[1]*HypergeometricPFQ[{}, {1/2, 3/4}, x^4/64] + (x*((2 + 2*I)*C[2]*Hy
pergeometricPFQ[{}, {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))

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)]