60.3.197 problem 1201

Internal problem ID [11207]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1201
Date solved : Monday, January 27, 2025 at 10:48:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(x^2*diff(diff(y(x),x),x)+x*(2*x+1)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \left (2 x +3\right ) {\mathrm e}^{-2 x}+2 c_{1} \left (x^{2}-2 x +\frac {3}{2}\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.291 (sec). Leaf size: 55

DSolve[-4*y[x] + x*(1 + 2*x)*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-2 x} (2 x+3) \left (c_2 \int _1^x\frac {4 e^{2 K[1]} K[1]^3}{(2 K[1]+3)^2}dK[1]+c_1\right )}{2 x^2} \]