83.48.2 problem Ex 2 page 97

Internal problem ID [19594]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 2 page 97
Date solved : Tuesday, January 28, 2025 at 02:01:14 PM
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&=\frac {2}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 58

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)=2/x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\frac {c_3}{\sqrt {x -1}\, \sqrt {x +1}}+c_{1} +\frac {\ln \left (x +\sqrt {x^{2}-1}\right ) c_{2}}{\sqrt {x^{2}-1}}-\frac {\arctan \left (\frac {1}{\sqrt {x^{2}-1}}\right )}{\sqrt {x^{2}-1}}}{x} \]

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 63

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]==2/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-\arctan \left (\frac {1}{\sqrt {x^2-1}}\right )-c_3 \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \sqrt {x^2-1}-c_2}{x \sqrt {x^2-1}} \]