Internal problem ID [9609]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1280.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)-(4*x^2+12*x+3)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-4 \,{\mathrm e}^{x} \operatorname {expIntegral}_{1}\left (2 x \right ) c_{2} x^{2}+\left (-1+2 x \right ) c_{2} {\mathrm e}^{-x}+c_{1} x^{2} {\mathrm e}^{x}}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 52
DSolve[(-3 - 12*x - 4*x^2)*y[x] + 8*x*y'[x] + 4*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 e^{-x} \left (4 e^{2 x} x^2 \operatorname {ExpIntegralEi}(-2 x)+2 x-1\right )}{2 x^{3/2}}+c_1 e^x \sqrt {x} \]