Internal problem ID [14763]
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 (c).
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)]`]]
\[ \boxed {\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^4-1)*diff(y(x),x$2)+(x^3-x)*diff(y(x),x)+(x^2-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\operatorname {arcsinh}\left (x \right )\right )+c_{2} \cos \left (\operatorname {arcsinh}\left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 43
DSolve[(x^4-1)*y''[x]+(x^3-x)*y'[x]+(x^2-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (\log \left (\sqrt {x^2+1}-x\right )\right )-c_2 \sin \left (\log \left (\sqrt {x^2+1}-x\right )\right ) \]