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 = 0.186197 (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 = 0.054 (sec), leaf count = 38
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,x^{8}}{\left (x^{2}-1\right )^{3}}+\frac {\textit {\_C2} \left (6 x^{4}-8 x^{2}+3\right )}{\left (x^{2}-1\right )^{3}}\right ]\] 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))
Maple raw output
[y(x) = _C1*x^8/(x^2-1)^3+_C2/(x^2-1)^3*(6*x^4-8*x^2+3)]