ODE
\[ 16 x^2 y''(x)+(4 x+3) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.178553 (sec), leaf count = 43
\[\left \{\left \{y(x)\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C1} \sin \left (\sqrt {x}\right ) x^{\frac {1}{4}}+\textit {\_C2} \,x^{\frac {1}{4}} \cos \left (\sqrt {x}\right )\right ]\] Mathematica raw input
DSolve[(3 + 4*x)*y[x] + 16*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(1/4)*(E^((2*I)*Sqrt[x])*C[1] + I*C[2]))/E^(I*Sqrt[x])}}
Maple raw input
dsolve(16*x^2*diff(diff(y(x),x),x)+(3+4*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sin(x^(1/2))*x^(1/4)+_C2*x^(1/4)*cos(x^(1/2))]