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 = 0.0605516 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {5 c_3+25 x^2+10 \log (x)+8}{5 x}+c_1 x \sin (\log (x))+c_2 x \cos (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.161 (sec), leaf count = 143
\[ \left \{ y \left ( x \right ) ={\frac {1}{5\,x} \left ( \left ( \left ( 5\,{\it \_C2}\,{x}^{2}-8 \right ) \cos \left ( \ln \left ( x \right ) \right ) +5\,{\it \_C3}\,{x}^{2}\sin \left ( \ln \left ( x \right ) \right ) +5\,{x}^{2}+5\,{\it \_C1}+10\,\ln \left ( x \right ) +6\,\sin \left ( \ln \left ( x \right ) \right ) \right ) \left ( \tan \left ( {\frac {\ln \left ( x \right ) }{2}} \right ) \right ) ^{2}+ \left ( -20\,{x}^{2}\cos \left ( \ln \left ( x \right ) \right ) +40\,{x}^{2}\sin \left ( \ln \left ( x \right ) \right ) +12\,\cos \left ( \ln \left ( x \right ) \right ) +16\,\sin \left ( \ln \left ( x \right ) \right ) \right ) \tan \left ( {\frac {\ln \left ( x \right ) }{2}} \right ) + \left ( 8+ \left ( 5\,{\it \_C2}+40 \right ) {x}^{2} \right ) \cos \left ( \ln \left ( x \right ) \right ) + \left ( -6+ \left ( 5\,{\it \_C3}+20 \right ) {x}^{2} \right ) \sin \left ( \ln \left ( x \right ) \right ) +5\,{x}^{2}+5\,{\it \_C1}+10\,\ln \left ( x \right ) \right ) \left ( 1+ \left ( \tan \left ( {\frac {\ln \left ( x \right ) }{2}} \right ) \right ) ^{2} \right ) ^{-1}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/5*(((5*_C2*x^2-8)*cos(ln(x))+5*_C3*x^2*sin(ln(x))+5*x^2+5*_C1+10*ln(x)+6*sin(ln(x)))*tan(1/2*ln(x))^2+(-20*x^2*cos(ln(x))+40*x^2*sin(ln(x))+12*cos(ln(x))+16*sin(ln(x)))*tan(1/2*ln(x))+(8+(5*_C2+40)*x^2)*cos(ln(x))+(-6+(5*_C3+20)*x^2)*sin(ln(x))+5*x^2+5*_C1+10*ln(x))/(1+tan(1/2*ln(x))^2)/x