Internal problem ID [12337]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{-x^{2}+4}=\sqrt {x}} \] With initial conditions \begin {align*} [y \left (1\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve([diff(y(x),x)=y(x)/(4-x^2)+sqrt(x),y(1) = -3],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x +2\right )^{\frac {1}{4}} \left (-2 \left (\int _{1}^{x}\frac {\left (\textit {\_z1} -2\right )^{\frac {1}{4}} \sqrt {\textit {\_z1}}}{\left (\textit {\_z1} +2\right )^{\frac {1}{4}}}d \textit {\_z1} \right )+\left (1+i\right ) \sqrt {2}\, 3^{\frac {3}{4}}\right )}{2 \left (x -2\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 158
DSolve[{y'[x]==y[x]/(4-x^2)+Sqrt[x],{y[1]==-3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x+2} \left (4 x^{3/2} \operatorname {AppellF1}\left (\frac {3}{2},\frac {3}{4},\frac {1}{4},\frac {5}{2},\frac {x}{2},-\frac {x}{2}\right )-12 \sqrt {x} \operatorname {AppellF1}\left (\frac {1}{2},\frac {3}{4},\frac {1}{4},\frac {3}{2},\frac {x}{2},-\frac {x}{2}\right )-4 \operatorname {AppellF1}\left (\frac {3}{2},\frac {3}{4},\frac {1}{4},\frac {5}{2},\frac {1}{2},-\frac {1}{2}\right )+12 \operatorname {AppellF1}\left (\frac {1}{2},\frac {3}{4},\frac {1}{4},\frac {3}{2},\frac {1}{2},-\frac {1}{2}\right )+6 \sqrt [4]{2-x} (x+2)^{3/4} \sqrt {x}-15\ 3^{3/4}\right )}{9 \sqrt [4]{2-x}} \]