Internal problem ID [10258]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear
equation. Page 114
Problem number: Ex 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+y^{\prime } x -y-x \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x^3*diff(y(x),x$3)+x*diff(y(x),x)-y(x)=x*ln(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \relax (x )^{4} x}{24}+c_{1} x +c_{2} x \ln \relax (x )+c_{3} \ln \relax (x )^{2} x \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 33
DSolve[x^3*y'''[x]+x*y'[x]-y[x]==x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} x \log ^4(x)+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \\ \end{align*}