Internal problem ID [7129]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 84.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=x^{2}-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 140
dsolve(diff(y(x),x)=x^2+y(x)^2-1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 c_{1} \operatorname {WhittakerW}\left (1+\frac {i}{4}, \frac {1}{4}, i x^{2}\right )}{x \left (c_{1} \operatorname {WhittakerW}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\operatorname {WhittakerM}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )\right )}-\frac {\left (2 c_{1} x^{2} i-c_{1} i-c_{1} \right ) \operatorname {WhittakerW}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\left (3+i\right ) \operatorname {WhittakerM}\left (1+\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\left (2 i x^{2}-i-1\right ) \operatorname {WhittakerM}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )}{2 x \left (c_{1} \operatorname {WhittakerW}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\operatorname {WhittakerM}\left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 153
DSolve[y'[x]==x^2+y[x]^2-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \left (x \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}-\frac {i}{2},(-1+i) x\right )+(1+i) \operatorname {ParabolicCylinderD}\left (\frac {1}{2}-\frac {i}{2},(-1+i) x\right )-c_1 x \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{2},(1+i) x\right )+(1-i) c_1 \operatorname {ParabolicCylinderD}\left (\frac {1}{2}+\frac {i}{2},(1+i) x\right )\right )}{\operatorname {ParabolicCylinderD}\left (-\frac {1}{2}-\frac {i}{2},(-1+i) x\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{2},(1+i) x\right )} y(x)\to \frac {(1+i) \operatorname {ParabolicCylinderD}\left (\frac {1}{2}+\frac {i}{2},(1+i) x\right )}{\operatorname {ParabolicCylinderD}\left (-\frac {1}{2}+\frac {i}{2},(1+i) x\right )}-i x \end{align*}