81.6.1 problem 1

Internal problem ID [18684]
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 : 1
Date solved : Tuesday, January 28, 2025 at 12:10:21 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime }&=\ln \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(x^3*diff(y(x),x$3)+7*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)=(ln(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )^{3}}{9}-\frac {4 \ln \left (x \right )^{2}}{9}-\frac {c_{2}}{x}+\frac {26 \ln \left (x \right )}{27}-\frac {c_{1}}{3 x^{3}}+c_3 \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 46

DSolve[x^3*D[y[x],{x,3}]+7*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]==(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {c_1}{3 x^3}+\frac {\log ^3(x)}{9}-\frac {4 \log ^2(x)}{9}+\frac {26 \log (x)}{27}-\frac {c_2}{x}+c_3 \]