Internal problem ID [14765]
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: 54 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([(x^4-1)*diff(y(x),x$2)+(x^3-x)*diff(y(x),x)+(x^2-1)*y(x)=0,y(0) = 0, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\sin \left (\operatorname {arcsinh}\left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 20
DSolve[{(x^4-1)*y''[x]+(x^3-x)*y'[x]+(x^2-1)*y[x]==0,{y[0]==0,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin \left (\log \left (\sqrt {x^2+1}-x\right )\right ) \]