ODE
\[ \left (x^2+1\right ) x^2 y'''(x)+8 x^3 y''(x)+10 x^2 y'(x)=3 x^2+2 x^2 \log (x)-1 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.115352 (sec), leaf count = 62
\[\left \{\left \{y(x)\to c_3-\frac {100 \left (3 c_2-1\right ) x^3+900 c_2 x+225 c_1+36 x^5-60 \left (3 x^4+10 x^2+15\right ) x \log (x)}{900 \left (x^2+1\right )^2}\right \}\right \}\]
Maple ✓
cpu = 0.18 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 180\,{x}^{5}+600\,{x}^{3}+900\,x \right ) \ln \left ( x \right ) -36\,{x}^{5}+900\,{\it \_C3}\,{x}^{4}+ \left ( -900\,{\it \_C1}+100 \right ) {x}^{3}+1800\,{\it \_C3}\,{x}^{2}-2700\,{\it \_C1}\,x-225\,{\it \_C2}+900\,{\it \_C3}}{900\, \left ( {x}^{2}+1 \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[10*x^2*y'[x] + 8*x^3*y''[x] + x^2*(1 + x^2)*y'''[x] == -1 + 3*x^2 + 2*x^2*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> C[3] - (36*x^5 + 225*C[1] + 900*x*C[2] + 100*x^3*(-1 + 3*C[2]) - 60*x*(15 + 10*x^2 + 3*x^4)*Log[x])/(900*(1 + x^2)^2)}}
Maple raw input
dsolve(x^2*(x^2+1)*diff(diff(diff(y(x),x),x),x)+8*x^3*diff(diff(y(x),x),x)+10*x^2*diff(y(x),x) = 2*x^2*ln(x)-1+3*x^2, y(x),'implicit')
Maple raw output
y(x) = 1/900*((180*x^5+600*x^3+900*x)*ln(x)-36*x^5+900*_C3*x^4+(-900*_C1+100)*x^3+1800*_C3*x^2-2700*_C1*x-225*_C2+900*_C3)/(x^2+1)^2