64.2.8 problem 5

Internal problem ID [13268]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:13:39 AM
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&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=0\\ y^{\prime }\left (2\right )&=2\\ y^{\prime \prime }\left (2\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

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)=0,y(2) = 0, D(y)(2) = 2, (D@@2)(y)(2) = 6],y(x), singsol=all)
 

\[ y = x^{3}-3 x^{2}+2 x \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 18

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]==0,{y[2]==0,Derivative[1][y][2]==2Derivative[2][y][2]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3}{4} x \left (x^2-8 x+12\right ) \]