62.36.4 problem Ex 4

Internal problem ID [13002]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:47:16 AM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve((x^3-x)*diff(y(x),x$3)+(8*x^2-3)*diff(y(x),x$2)+14*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\frac {c_{3}}{\sqrt {x +1}\, \sqrt {x -1}}+c_{1} +\frac {c_{2} \ln \left (x +\sqrt {x^{2}-1}\right )}{\sqrt {x^{2}-1}}}{x} \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 68

DSolve[(x^3-x)*D[y[x],{x,3}]+(8*x^2-3)*D[y[x],{x,2}]+14*x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_3 \arcsin (x) \csc \left (\frac {1}{2} (2 \arcsin (x)+\pi )\right )+c_3 \log \left (\cos \left (\frac {1}{4} (2 \arcsin (x)+\pi )\right )\right )-\frac {c_2}{\sqrt {x^2-1}}-\frac {1}{2} c_3 \log (1-x)+c_1}{x} \]