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 = 0.0353732 (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 = 0.025 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) =\sqrt [4]{x} \left ( \sin \left ( \sqrt {x} \right ) {\it \_C1}+\cos \left ( \sqrt {x} \right ) {\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^(1/4)*(sin(x^(1/2))*_C1+cos(x^(1/2))*_C2)