Internal problem ID [2262]
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: 13.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y=x +\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(4*x^3*diff(y(x),x$3)+8*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x+ln(x),y(x), singsol=all)
\[ y = \frac {\ln \left (x \right ) x}{3}+\ln \left (x \right )+1-\frac {8 x}{9}+c_{1} x +\frac {c_{2}}{\sqrt {x}}+c_{3} \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 40
DSolve[4*x^3*y'''[x]+8*x^2*y''[x]-x*y'[x]+y[x]==x+Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} (x+3) \log (x)+\frac {c_1}{\sqrt {x}}+c_2 \sqrt {x}+\left (-\frac {8}{9}+c_3\right ) x+1 \]