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))]