7.9.7 problem 19

Internal problem ID [255]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:42:57 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 (1\right )&=6\\ y^{\prime }\left (1\right )&=14\\ y^{\prime \prime }\left (1\right )&=22 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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(1) = 6, D(y)(1) = 14, (D@@2)(y)(1) = 22],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 17

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[1]==6,Derivative[1][y][1] ==14,Derivative[2][y][1] ==22}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (3 x^2+2 x+1\right ) \]