83.8.29 problem 30

Internal problem ID [19155]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 01:10:26 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 56

dsolve(diff(y(x),x)+y(x)/(1-x^2)^(3/2)= (x+sqrt(1-x^2))/(1-x^2)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\int \frac {{\mathrm e}^{\frac {x}{\sqrt {-x^{2}+1}}} \left (x +\sqrt {-x^{2}+1}\right )}{\left (x -1\right )^{2} \left (x +1\right )^{2}}d x +c_{1} \right ) {\mathrm e}^{-\frac {x}{\sqrt {-x^{2}+1}}} \]

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 38

DSolve[D[y[x],x]+y[x]/(1-x^2)^(3/2)== (x+Sqrt[1-x^2])/(1-x^2)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x}{\sqrt {1-x^2}}+c_1 e^{-\frac {x}{\sqrt {1-x^2}}} \]