4.44.11 \(x y'''(x)+x^2 (-y(x))+3 y''(x)=0\)

ODE
\[ x y'''(x)+x^2 (-y(x))+3 y''(x)=0 \] ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.03381 (sec), leaf count = 77

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

Maple ✓
cpu = 0.093 (sec), leaf count = 45

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_0$F$_2$}(\ ;\,{\frac {3}{4}},{\frac {5}{4}};\,{\frac {{x}^{4}}{64}})}+{\frac {{\it \_C2}}{x}{\mbox {$_0$F$_2$}(\ ;\,{\frac {1}{2}},{\frac {3}{4}};\,{\frac {{x}^{4}}{64}})}}+{\it \_C3}\,x{\mbox {$_0$F$_2$}(\ ;\,{\frac {5}{4}},{\frac {3}{2}};\,{\frac {{x}^{4}}{64}})} \right \} \] Mathematica raw input

DSolve[-(x^2*y[x]) + 3*y''[x] + x*y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ((2 - 2*I)*C[1]*HypergeometricPFQ[{}, {1/2, 3/4}, x^4/64])/x + C[2]*Hy
pergeometricPFQ[{}, {3/4, 5/4}, x^4/64] + (1/4 + I/4)*x*C[3]*HypergeometricPFQ[{
}, {5/4, 3/2}, x^4/64]}}

Maple raw input

dsolve(x*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-x^2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*hypergeom([],[3/4, 5/4],1/64*x^4)+_C2/x*hypergeom([],[1/2, 3/4],1/64*
x^4)+_C3*x*hypergeom([],[5/4, 3/2],1/64*x^4)