7.9.8 problem 20

Internal problem ID [256]
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 : 20
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 }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=5\\ y^{\prime \prime }\left (1\right )&=-11 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

dsolve([x^3*diff(y(x),x$3)+6*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)-4*y(x)=0,y(1) = 1, D(y)(1) = 5, (D@@2)(y)(1) = -11],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

DSolve[{x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==0,{y[1]==1,Derivative[1][y][1] ==5,Derivative[2][y][1] ==-11}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x^3+\log (x)-1}{x^2} \]