\[ -f(x)+x^2 y^{(3)}(x)+\left (x^2+2\right ) y'(x)+4 x y''(x)+3 x y(x)=0 \] ✓ Mathematica : cpu = 1.07985 (sec), leaf count = 479
DSolve[-f[x] + 3*x*y[x] + (2 + x^2)*Derivative[1][y][x] + 4*x*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {2 \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {x^2}{4}\right ) \int _1^x\frac {9 \pi (\operatorname {BesselJ}(1,K[3]) \operatorname {BesselY}(0,K[3])-\operatorname {BesselJ}(0,K[3]) \operatorname {BesselY}(1,K[3])) f(K[3]) K[3]^2}{2 \left (16 \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[3]^2\right ) K[3]^4-9 \pi \pmb {H}_0(K[3]) K[3]^3+18 K[3]^2-9 \pi \pmb {H}_0(K[3]) K[3]+18\right )}dK[3]+x \operatorname {BesselJ}(0,x) \int _1^x-\frac {9 \left (2 \pi \operatorname {BesselY}(0,K[1]) f(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-\pi \operatorname {BesselY}(1,K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+\pi \operatorname {BesselY}(0,K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )\right )}{16 \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[1]^2\right ) K[1]^4-9 \pi \pmb {H}_0(K[1]) K[1]^3+18 K[1]^2-9 \pi \pmb {H}_0(K[1]) K[1]+18}dK[1]+2 x \operatorname {BesselY}(0,x) \int _1^x\frac {9 \left (2 \pi \operatorname {BesselJ}(0,K[2]) f(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2-\pi \operatorname {BesselJ}(1,K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]+\pi \operatorname {BesselJ}(0,K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )\right )}{2 \left (16 \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[2]^2\right ) K[2]^4-9 \pi \pmb {H}_0(K[2]) K[2]^3+18 K[2]^2-9 \pi \pmb {H}_0(K[2]) K[2]+18\right )}dK[2]}{x}+\frac {2 c_3 \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {x^2}{4}\right )}{x}+c_1 \operatorname {BesselJ}(0,x)+2 c_2 \operatorname {BesselY}(0,x)\right \}\right \}\] ✓ Maple : cpu = 0.371 (sec), leaf count = 1032
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+4*x*diff(diff(y(x),x),x)+(x^2+2)*diff(y(x),x)+3*x*y(x)-f(x)=0,y(x))
\[\text {Expression too large to display}\]