ODE
\[ 4 x^2 y''(x)+y(x)=\sqrt {x} \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.166344 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {1}{8} \sqrt {x} \left (\log ^2(x)+4 c_2 \log (x)+8 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 26
\[\left [y \left (x \right ) = \sqrt {x}\, \textit {\_C2} +\sqrt {x}\, \ln \left (x \right ) \textit {\_C1} +\frac {\ln \left (x \right )^{2} \sqrt {x}}{8}\right ]\] Mathematica raw input
DSolve[y[x] + 4*x^2*y''[x] == Sqrt[x],y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[x]*(8*C[1] + 4*C[2]*Log[x] + Log[x]^2))/8}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+y(x) = x^(1/2), y(x))
Maple raw output
[y(x) = x^(1/2)*_C2+x^(1/2)*ln(x)*_C1+1/8*ln(x)^2*x^(1/2)]