Internal problem ID [14746]
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: 37.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1, y^{\prime \prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([x^3*diff(y(x),x$3)-2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)-5*y(x)=0,y(1) = 0, D(y)(1) = -1, (D@@2)(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 x \left (x \cos \left (\ln \left (x \right )\right )-\frac {\sin \left (\ln \left (x \right )\right ) x}{3}-1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[{x^3*y'''[x]-2*x^2*y''[x]+5*x*y'[x]-5*y[x]==0,{y[1]==0,y'[1]==-1,y''[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} x (-x \sin (\log (x))+3 x \cos (\log (x))-3) \]