ODE
\[ 4 x^2 y''(x)+y(x)=\sqrt {x} \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0148032 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {1}{8} \sqrt {x} \left (4 c_2 \log (x)+8 c_1+\log ^2(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\frac { \left ( \ln \left ( x \right ) \right ) ^{2}+8\,\ln \left ( x \right ) {\it \_C1}+8\,{\it \_C2}}{8}\sqrt {x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/8*x^(1/2)*(ln(x)^2+8*ln(x)*_C1+8*_C2)