ODE
\[ f(x) y'(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.192473 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \int _1^x\exp \left (\int _1^{K[2]}-f(K[1])dK[1]\right ) c_1dK[2]+c_2\right \}\right \}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} +\left (\int {\mathrm e}^{\int -f \left (x \right )d x}d x \right ) \textit {\_C2}]\] Mathematica raw input
DSolve[f[x]*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2] + Inactive[Integrate][E^Inactive[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))
Maple raw output
[y(x) = _C1+Int(exp(Int(-f(x),x)),x)*_C2]