Internal problem ID [14745]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y=0} \] 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: 0.031 (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)
\[ y \left (x \right ) = -\frac {35}{2 x^{3}}+\frac {3}{2 x^{7}}+\frac {21}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[{x^3*y'''[x]+15*x^2*y''[x]+54*x*y'[x]+42*y[x]==0,{y[1]==5,y'[1]==0,y''[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {42 x^5-35 x^4+3}{2 x^7} \]