62.32.2 problem Ex 2

Internal problem ID [12979]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:46:11 AM
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: 0.004 (sec). Leaf size: 29

dsolve((x-3)*diff(y(x),x$2)-(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: 0.185 (sec). Leaf size: 90

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

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