ODE
\[ f(x) y'(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.552011 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \int _1^x c_1 e^{\int _1^{K[2]} -f(K[1]) \, dK[1]} \, dK[2]+c_2\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}+\int \!{{\rm e}^{\int \!-f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x{\it \_C2} \right \} \] Mathematica raw input
DSolve[f[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2] + Integrate[E^Integrate[-f[K[1]], {K[1], 1, K[2]}]*C[1], {K[2], 1, x}]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+f(x)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+Int(exp(Int(-f(x),x)),x)*_C2