81.6.5 problem 5

Internal problem ID [18688]
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 : 5
Date solved : Tuesday, January 28, 2025 at 12:10:24 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$3)+4*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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