38.2.44 problem 44

Internal problem ID [6473]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 44
Date solved : Monday, January 27, 2025 at 02:07:07 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x)+(1/x-(2*x)/(1-x^2))*y(x)=1/(1-x^2),y(x), singsol=all)
 

\[ y = \frac {-x^{2}+2 c_1}{2 x^{3}-2 x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 25

DSolve[D[y[x],x]+(1/x-(2*x)/(1-x^2))*y[x]==1/(1-x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2+2 c_1}{2 x-2 x^3} \]