60.3.125 problem 1129

Internal problem ID [11135]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1129
Date solved : Monday, January 27, 2025 at 10:46:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve((x-3)*diff(diff(y(x),x),x)-(4*x-9)*diff(y(x),x)+(3*x-6)*y(x)=0,y(x), singsol=all)
 

\[ y = 4 c_{2} \left (x^{3}-\frac {21}{2} x^{2}+\frac {75}{2} x -\frac {183}{4}\right ) {\mathrm e}^{3 x}+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 90

DSolve[(-6 + 3*x)*y[x] - (-9 + 4*x)*D[y[x],x] + (-3 + x)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {3}{6-2 K[1]}-1\right )dK[1]-\frac {1}{2} \int _1^x\left (-4-\frac {3}{K[2]-3}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3-2 K[1]}{2 (K[1]-3)}dK[1]\right )dK[3]+c_1\right ) \]