62.28.1 problem Ex 1

Internal problem ID [12948]
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
Date solved : Tuesday, January 28, 2025 at 04:44:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

\[ y = x \left (\frac {\ln \left (x \right )^{4}}{24}+c_{1} +\ln \left (x \right ) c_{2} +c_3 \ln \left (x \right )^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{24} x \log ^4(x)+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \]