Internal problem ID [14744]
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: 35.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1, y^{\prime \prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([x^3*diff(y(x),x$3)+10*x^2*diff(y(x),x$2)-20*x*diff(y(x),x)+20*y(x)=0,y(1) = 0, D(y)(1) = -1, (D@@2)(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {8 x}{11}+\frac {1}{44 x^{10}}-\frac {3 x^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[{x^3*y'''[x]+10*x^2*y''[x]-20*x*y'[x]+20*y[x]==0,{y[1]==0,y'[1]==-1,y''[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{44 x^{10}}-\frac {3 x^2}{4}+\frac {8 x}{11} \]