Internal problem ID [7136]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=x^{2}+x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 155
dsolve(diff(y(x),x)-y(x)^2-x-x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \left (i x^{2}+i x -1+\frac {1}{4} i\right ) c_{1} \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+2 \left (\left (-\frac {1}{12}-i\right ) c_{1} \left (x +\frac {1}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {7}{4}-\frac {i}{16}\right ], \left [\frac {5}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\left (-\frac {1}{8}-\frac {i}{2}\right ) \operatorname {hypergeom}\left (\left [\frac {5}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\frac {i \operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )}{2}\right ) \left (x +\frac {1}{2}\right )}{\left (2 x +1\right ) c_{1} \operatorname {hypergeom}\left (\left [\frac {3}{4}-\frac {i}{16}\right ], \left [\frac {3}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )+\operatorname {hypergeom}\left (\left [\frac {1}{4}-\frac {i}{16}\right ], \left [\frac {1}{2}\right ], \frac {i \left (2 x +1\right )^{2}}{4}\right )} \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 298
DSolve[y'[x]-y[x]^2-x-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \left ((2 x+1) \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}-\frac {i}{8},\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )-c_1 (2 x+1) \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )+(2+2 i) \left (\operatorname {ParabolicCylinderD}\left (\frac {1}{2}-\frac {i}{8},\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )-i c_1 \operatorname {ParabolicCylinderD}\left (\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )\right )\right )}{2 \left (\operatorname {ParabolicCylinderD}\left (-\frac {1}{2}-\frac {i}{8},\left (-\frac {1}{2}+\frac {i}{2}\right ) (2 x+1)\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )\right )} \\ y(x)\to \frac {(1+i) \operatorname {ParabolicCylinderD}\left (\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}{\operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}-\frac {1}{2} i (2 x+1) \\ y(x)\to \frac {(1+i) \operatorname {ParabolicCylinderD}\left (\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}{\operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{8},(1+i) x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )}-\frac {1}{2} i (2 x+1) \\ \end{align*}