12.17.6 problem section 9.1, problem 5(b)

Internal problem ID [2112]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
Problem number : section 9.1, problem 5(b)
Date solved : Monday, January 27, 2025 at 05:42:34 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=k_{0}\\ y^{\prime }\left (1\right )&=k_{1}\\ y^{\prime \prime }\left (1\right )&=k_{2} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 40

dsolve([x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+6*y(x)=0,y(1) = k__0, D(y)(1) = k__1, (D@@2)(y)(1) = k__2],y(x), singsol=all)
 

\[ y = \frac {3 \left (-2 k_{0} +k_{2} \right ) x^{4}+4 \left (k_{1} +3 k_{0} -k_{2} \right ) x^{3}+6 k_{0} -4 k_{1} +k_{2}}{12 x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 47

DSolve[{x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+6*y[x]==0,{y[1]==k0,Derivative[1][y][1]==k1,Derivative[2][y][1]==k2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-6 \text {k0} \left (x^4-2 x^3-1\right )+4 \text {k1} \left (x^3-1\right )+3 \text {k2} x^4-4 \text {k2} x^3+\text {k2}}{12 x} \]