81.6.3 problem 3

Internal problem ID [18686]
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 : 3
Date solved : Tuesday, January 28, 2025 at 12:10:23 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 30

dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-6*y(x)=x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 34

DSolve[x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]-6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^3 \log (x)+x \left (\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1\right ) \]