Internal problem ID [2261]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y=\left (x -1\right ) \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 44
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)
\[ y \left (x \right ) = \frac {\sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{2}}{x^{\frac {3}{2}}}+\frac {\cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) c_{1}}{x^{\frac {3}{2}}}+\frac {1}{3}+\frac {\left (3 x -7\right ) \ln \left (x \right )}{21}-\frac {5 x}{49} \]
✓ Solution by Mathematica
Time used: 0.516 (sec). Leaf size: 67
DSolve[x^2*y''[x]+4*x*y'[x]+3*y[x]==(x-1)*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{x^{3/2}}+\frac {c_1 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )}{x^{3/2}}-\frac {5 x}{49}+\frac {1}{7} x \log (x)-\frac {\log (x)}{3}+\frac {1}{3} \]