82.54.5 problem Ex. 5

Internal problem ID [19021]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 5
Date solved : Tuesday, January 28, 2025 at 12:45:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

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

dsolve([(x-3)*diff(y(x),x$2)-(4*x-9)*diff(y(x),x)+3*(x-2)*y(x)=0,exp(x)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 42

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

\[ y(x)\to \frac {1}{8} c_2 e^{3 x-9} \left (4 x^3-42 x^2+150 x-183\right )+c_1 e^{x-3} \]