62.29.12 problem Ex 14

Internal problem ID [12963]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 14
Date solved : Tuesday, January 28, 2025 at 04:45:33 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 33

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

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