81.6.14 problem 14

Internal problem ID [18697]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 12:10:41 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }&=-\frac {1}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$3)+5*x*diff(y(x),x$2)+4*diff(y(x),x)=-1/x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 40

DSolve[x^2*D[y[x],{x,3}]+5*x*D[y[x],{x,2}]+4*D[y[x],x]==-1/x^2,y[x],x,IncludeSingularSolutions -> True]
 

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