Internal problem ID [12428]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\sqrt {1-x}\, y^{\prime \prime }-4 y=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (-2\right ) = 3, y^{\prime }\left (-2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.562 (sec). Leaf size: 185
dsolve([sqrt(1-x)*diff(y(x),x$2)-4*y(x)=sin(x),y(-2) = 3, D(y)(-2) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {8 \pi \left (\frac {\left (\left (\int _{-2}^{x}\frac {\sin \left (\textit {\_z1} \right ) \sqrt {1-\textit {\_z1}}\, \operatorname {BesselI}\left (\frac {2}{3}, \frac {8 \sqrt {\left (1-\textit {\_z1} \right )^{\frac {3}{2}}}}{3}\right )}{\left (\left (1-\textit {\_z1} \right )^{\frac {3}{2}}\right )^{\frac {1}{3}}}d \textit {\_z1} \right ) \sqrt {3}+6 \operatorname {BesselI}\left (-\frac {1}{3}, \frac {8 \,3^{\frac {3}{4}}}{3}\right ) 3^{\frac {3}{4}}-3 \operatorname {BesselI}\left (\frac {2}{3}, \frac {8 \,3^{\frac {3}{4}}}{3}\right )\right ) \left (\left (1-x \right )^{\frac {3}{2}}\right )^{\frac {2}{3}} \operatorname {BesselI}\left (-\frac {2}{3}, \frac {8 \sqrt {\left (1-x \right )^{\frac {3}{2}}}}{3}\right )}{6}+\left (\operatorname {BesselI}\left (\frac {1}{3}, \frac {8 \,3^{\frac {3}{4}}}{3}\right ) 3^{\frac {3}{4}}+\frac {\left (\int _{-2}^{x}\frac {\operatorname {BesselI}\left (-\frac {2}{3}, \frac {8 \sqrt {\left (1-\textit {\_z1} \right )^{\frac {3}{2}}}}{3}\right ) \left (\left (1-\textit {\_z1} \right )^{\frac {3}{2}}\right )^{\frac {1}{3}} \sin \left (\textit {\_z1} \right )}{\sqrt {1-\textit {\_z1}}}d \textit {\_z1} \right ) \sqrt {3}}{6}-\frac {\operatorname {BesselI}\left (-\frac {2}{3}, \frac {8 \,3^{\frac {3}{4}}}{3}\right )}{2}\right ) \operatorname {BesselI}\left (\frac {2}{3}, \frac {8 \sqrt {\left (1-x \right )^{\frac {3}{2}}}}{3}\right ) \left (x -1\right )\right )}{3 \left (\left (1-x \right )^{\frac {3}{2}}\right )^{\frac {1}{3}}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{Sqrt[1-x]*y''[x]-4*y[x]==Sin[x],{y[-2]==3,y'[-2]==-1}},y[x],x,IncludeSingularSolutions -> True]
Not solved