Internal problem ID [12704]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number: 4 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{-x^{2}+1}=\sqrt {x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 98
dsolve(diff(y(x),x)=y(x)/(1-x^2)+sqrt(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (1+x \right ) c_{1}}{\sqrt {-x^{2}+1}}+\frac {-2 \sqrt {1+x}\, \sqrt {2-2 x}\, \sqrt {-x}\, \operatorname {EllipticF}\left (\sqrt {1+x}, \frac {\sqrt {2}}{2}\right )+6 \sqrt {1+x}\, \sqrt {2-2 x}\, \sqrt {-x}\, \operatorname {EllipticE}\left (\sqrt {1+x}, \frac {\sqrt {2}}{2}\right )+2 x^{3}-2 x}{\sqrt {x}\, \left (3 x -3\right )} \]
✓ Solution by Mathematica
Time used: 1.157 (sec). Leaf size: 100
DSolve[y'[x]==y[x]/(1-x^2)+Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\frac {2 x \left (-\sqrt {1-x^2} x \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {3}{4},\frac {7}{4},x^2\right )+\sqrt {1-x^2} \operatorname {Hypergeometric2F1}\left (\frac {1}{4},\frac {1}{2},\frac {5}{4},x^2\right )+x^2-1\right )}{\sqrt {-((x-1) x)}}+3 c_1 \sqrt {x+1}}{3 \sqrt {1-x}} \]