4.45.3 $$x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )$$

ODE
$x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )$ ODE Classiﬁcation

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.223113 (sec), leaf count = 42

$\left \{\left \{y(x)\to \frac {25 x^2+10 \log (x)+8+5 c_3}{5 x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x))\right \}\right \}$

Maple
cpu = 1.444 (sec), leaf count = 179

$\left [y \left (x \right ) = \frac {20 \left (\cos ^{2}\left (\ln \left (x \right )\right )\right ) \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right ) x^{2}+20 \left (\sin ^{2}\left (\ln \left (x \right )\right )\right ) \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right ) x^{2}+20 \left (\cos ^{2}\left (\ln \left (x \right )\right )\right ) x^{2}+20 \left (\sin ^{2}\left (\ln \left (x \right )\right )\right ) x^{2}+5 \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right ) x^{2}-8 \cos \left (\ln \left (x \right )\right ) \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right )+6 \sin \left (\ln \left (x \right )\right ) \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right )+10 \ln \left (x \right ) \left (\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right )+12 \cos \left (\ln \left (x \right )\right ) \tan \left (\frac {\ln \left (x \right )}{2}\right )+16 \sin \left (\ln \left (x \right )\right ) \tan \left (\frac {\ln \left (x \right )}{2}\right )+5 x^{2}+8 \cos \left (\ln \left (x \right )\right )-6 \sin \left (\ln \left (x \right )\right )+10 \ln \left (x \right )}{5 x \left (1+\tan ^{2}\left (\frac {\ln \left (x \right )}{2}\right )\right )}+\frac {\textit {\_C1}}{x}+\textit {\_C2} x \cos \left (\ln \left (x \right )\right )+\textit {\_C3} x \sin \left (\ln \left (x \right )\right )\right ]$ Mathematica raw input

DSolve[2*x*y[x] + 2*x^3*y''[x] + x^4*y'''[x] == 10*(1 + x^2),y[x],x]

Mathematica raw output

{{y[x] -> x*C[2]*Cos[Log[x]] + (8 + 25*x^2 + 5*C[3] + 10*Log[x])/(5*x) + x*C[1]*
Sin[Log[x]]}}

Maple raw input

dsolve(x^4*diff(diff(diff(y(x),x),x),x)+2*x^3*diff(diff(y(x),x),x)+2*x*y(x) = 10*x^2+10, y(x))

Maple raw output

[y(x) = 1/5/x*(20*cos(ln(x))^2*tan(1/2*ln(x))^2*x^2+20*sin(ln(x))^2*tan(1/2*ln(x
))^2*x^2+20*cos(ln(x))^2*x^2+20*sin(ln(x))^2*x^2+5*tan(1/2*ln(x))^2*x^2-8*cos(ln
(x))*tan(1/2*ln(x))^2+6*sin(ln(x))*tan(1/2*ln(x))^2+10*ln(x)*tan(1/2*ln(x))^2+12
*cos(ln(x))*tan(1/2*ln(x))+16*sin(ln(x))*tan(1/2*ln(x))+5*x^2+8*cos(ln(x))-6*sin
(ln(x))+10*ln(x))/(1+tan(1/2*ln(x))^2)+1/x*_C1+_C2*x*cos(ln(x))+_C3*x*sin(ln(x))
]