Internal problem ID [14747]
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: 38.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -2, y^{\prime }\left (1\right ) = 0, y^{\prime \prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 24
dsolve([x^3*diff(y(x),x$3)-6*x^2*diff(y(x),x$2)+17*x*diff(y(x),x)-17*y(x)=0,y(1) = -2, D(y)(1) = 0, (D@@2)(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-11 \sin \left (\ln \left (x \right )\right )+7 \cos \left (\ln \left (x \right )\right )\right ) x^{4}}{5}-\frac {17 x}{5} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[{x^3*y'''[x]-6*x^2*y''[x]+17*x*y'[x]-17*y[x]==0,{y[1]==-2,y'[1]==0,y''[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} x \left (-11 x^3 \sin (\log (x))+7 x^3 \cos (\log (x))-17\right ) \]