15.16.12 problem 12

Internal problem ID [3232]
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 : 12
Date solved : Monday, January 27, 2025 at 07:27:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y&=\left (x -1\right ) \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 43

dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+3*y(x)=(x-1)*ln(x),y(x), singsol=all)
 

\[ y = \frac {1}{3}+\frac {\left (3 x -7\right ) \ln \left (x \right )}{21}-\frac {5 x}{49}+\frac {\cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{1} +\sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_2}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.581 (sec). Leaf size: 67

DSolve[x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+3*y[x]==(x-1)*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{x^{3/2}}+\frac {c_1 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{x^{3/2}}-\frac {5 x}{49}+\frac {1}{7} x \log (x)-\frac {\log (x)}{3}+\frac {1}{3} \]