60.3.194 problem 1198

Internal problem ID [11204]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1198
Date solved : Monday, January 27, 2025 at 10:48:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(x^2*diff(diff(y(x),x),x)-(x^2-2*x)*diff(y(x),x)-(3*x+2)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 34

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

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