15.16.5 problem 5

Internal problem ID [3225]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 5
Date solved : Monday, January 27, 2025 at 07:26:42 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y&=\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)-18*y(x)=ln(x),y(x), singsol=all)
 

\[ y = x^{{9}/{2}} c_2 +\frac {c_{1}}{x^{2}}-\frac {\ln \left (x \right )}{18}+\frac {5}{324} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 29

DSolve[2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]-18*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{9/2}+\frac {c_1}{x^2}-\frac {\log (x)}{18}+\frac {5}{324} \]