81.6.13 problem 13

Internal problem ID [18696]
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 : 13
Date solved : Tuesday, January 28, 2025 at 12:10:41 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve((x^3+x^2-3*x+1)*diff(y(x),x$3)+(9*x^2+6*x-9)*diff(y(x),x$2)+(18*x+6)*diff(y(x),x)+6*y(x)=x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{6}+120 c_{1} x^{2}+120 c_{2} x +120 c_3}{120 \left (x -1\right ) \left (x^{2}+2 x -1\right )} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 42

DSolve[(x^3+x^2-3*x+1)*D[y[x],{x,3}]+(9*x^2+6*x-9)*D[y[x],{x,2}]+(18*x+6)*D[y[x],x]+6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^6+60 c_3 x^2+120 c_2 x+120 c_1}{120 \left (x^3+x^2-3 x+1\right )} \]