60.3.262 problem 1267

Internal problem ID [11272]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1267
Date solved : Monday, January 27, 2025 at 11:04:47 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.282 (sec). Leaf size: 47

dsolve(2*x^2*diff(diff(y(x),x),x)-(2*x^2+l-5*x)*diff(y(x),x)-(4*x-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.581 (sec). Leaf size: 59

DSolve[(1 - 4*x)*y[x] - (l - 5*x + 2*x^2)*D[y[x],x] + 2*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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