74.15.36 problem 36

Internal problem ID [16475]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 09:08:56 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=0\\ y^{\prime \prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 20

dsolve([x^3*diff(y(x),x$3)+15*x^2*diff(y(x),x$2)+54*x*diff(y(x),x)+42*y(x)=0,y(1) = 5, D(y)(1) = 0, (D@@2)(y)(1) = 0],y(x), singsol=all)
 

\[ y = -\frac {35}{2 x^{3}}+\frac {3}{2 x^{7}}+\frac {21}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 24

DSolve[{x^3*D[y[x],{x,3}]+15*x^2*D[y[x],{x,2}]+54*x*D[y[x],x]+42*y[x]==0,{y[1]==5,Derivative[1][y][1]==0,Derivative[2][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {42 x^5-35 x^4+3}{2 x^7} \]