83.36.5 problem 5

Internal problem ID [19439]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (A) at page 125
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:42:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve((3-x)*diff(y(x),x$2)-(9-4*x)*diff(y(x),x)+(6-3*x)*y(x)=0,y(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: 0.049 (sec). Leaf size: 42

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

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