Internal problem ID [12656]
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: 20.
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 (3\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 41
dsolve([diff(y(x),x)=y(x)/(4-x^2)+sqrt(x),y(3) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 \,5^{\frac {3}{4}}+5 \left (\int _{3}^{x}\frac {\sqrt {\textit {\_z1}}\, \left (\textit {\_z1} -2\right )^{\frac {1}{4}}}{\left (2+\textit {\_z1} \right )^{\frac {1}{4}}}d \textit {\_z1} \right )\right ) \left (x +2\right )^{\frac {1}{4}}}{5 \left (x -2\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 2.843 (sec). Leaf size: 202
DSolve[{y'[x]==y[x]/(4-x^2)+Sqrt[x],{y[3]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (\frac {1}{45}+\frac {i}{45}\right ) \sqrt [4]{x+2} \left ((10-10 i) x^{3/2} \operatorname {AppellF1}\left (\frac {3}{2},\frac {3}{4},\frac {1}{4},\frac {5}{2},\frac {x}{2},-\frac {x}{2}\right )-(30-30 i) \sqrt {x} \operatorname {AppellF1}\left (\frac {1}{2},\frac {3}{4},\frac {1}{4},\frac {3}{2},\frac {x}{2},-\frac {x}{2}\right )-3 \left ((10-10 i) \sqrt {3} \operatorname {AppellF1}\left (\frac {3}{2},\frac {3}{4},\frac {1}{4},\frac {5}{2},\frac {3}{2},-\frac {3}{2}\right )-(10-10 i) \sqrt {3} \operatorname {AppellF1}\left (\frac {1}{2},\frac {3}{4},\frac {1}{4},\frac {3}{2},\frac {3}{2},-\frac {3}{2}\right )+(-5+5 i) \sqrt [4]{2-x} \sqrt {x} (x+2)^{3/4}+5\ 5^{3/4} \sqrt {6}-6 \sqrt {2} 5^{3/4}\right )\right )}{\sqrt [4]{2-x}} \]