15.16.6 problem 6

Internal problem ID [3226]
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 : 6
Date solved : Monday, January 27, 2025 at 07:26:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \frac {5}{2}+\frac {\ln \left (x^{2}\right )}{2}+\frac {2 c_{1} x^{2}}{3}+\sqrt {x}\, c_2 \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{2} \left (\log \left (x^2\right )+5\right )+c_2 x^2+c_1 \sqrt {x} \]