60.3.275 problem 1280

Internal problem ID [11285]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1280
Date solved : Monday, January 27, 2025 at 11:05:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = \frac {-4 \,{\mathrm e}^{x} \operatorname {Ei}_{1}\left (2 x \right ) c_{2} x^{2}+\left (-1+2 x \right ) c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x} x^{2}}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.298 (sec). Leaf size: 38

DSolve[(-3 - 12*x - 4*x^2)*y[x] + 8*x*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \sqrt {x} \left (c_2 \int _1^x\frac {e^{-2 K[1]}}{K[1]^3}dK[1]+c_1\right ) \]