60.3.249 problem 1254

Internal problem ID [11259]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1254
Date solved : Monday, January 27, 2025 at 11:00:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 44

dsolve((x^2+x-2)*diff(diff(y(x),x),x)+(x^2-x)*diff(y(x),x)-(6*x^2+7*x)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-3 x} \left (195 \,{\mathrm e}^{5 x -5} c_{2} \left (x -1\right ) \operatorname {Ei}_{1}\left (5 x -5\right )+\left (x -1\right ) c_{1} {\mathrm e}^{5 x}-c_{2} \left (x +44\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 97

DSolve[(-7*x - 6*x^2)*y[x] + (-x + x^2)*D[y[x],x] + (-2 + x + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (-\frac {1}{K[1]+2}+\frac {5}{2}+\frac {1}{K[1]-1}\right )dK[1]-\frac {1}{2} \int _1^x\frac {K[2]}{K[2]+2}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\left (-\frac {1}{K[1]+2}+\frac {5}{2}+\frac {1}{K[1]-1}\right )dK[1]\right )dK[3]+c_1\right ) \]