ODE
\[ x \left (1-x^2\right ) y''(x)-\left (x^2+7\right ) y'(x)+4 x y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0409576 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \frac {-24 c_1 x^8+6 c_2 x^4-8 c_2 x^2+3 c_2}{24 \left (x^2-1\right )^3}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{8}+6\,{\it \_C2}\,{x}^{4}-8\,{\it \_C2}\,{x}^{2}+3\,{\it \_C2}}{ \left ( {x}^{2}-1 \right ) ^{3}}} \right \} \] Mathematica raw input
DSolve[4*x*y[x] - (7 + x^2)*y'[x] + x*(1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-24*x^8*C[1] + 3*C[2] - 8*x^2*C[2] + 6*x^4*C[2])/(24*(-1 + x^2)^3)}}
Maple raw input
dsolve(x*(-x^2+1)*diff(diff(y(x),x),x)-(x^2+7)*diff(y(x),x)+4*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*x^8+6*_C2*x^4-8*_C2*x^2+3*_C2)/(x^2-1)^3