Internal problem ID [6376]
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]
Solve \begin {gather*} \boxed {y^{\prime }+1-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 140
dsolve(diff(y(x),x)=x^2+y(x)^2-1,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 c_{1} \WhittakerW \left (1+\frac {i}{4}, \frac {1}{4}, i x^{2}\right )}{x \left (c_{1} \WhittakerW \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\WhittakerM \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )\right )}-\frac {\left (2 i c_{1} x^{2}-i c_{1}-c_{1}\right ) \WhittakerW \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\left (3+i\right ) \WhittakerM \left (1+\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\left (2 i x^{2}-i-1\right ) \WhittakerM \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )}{2 x \left (c_{1} \WhittakerW \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )+\WhittakerM \left (\frac {i}{4}, \frac {1}{4}, i x^{2}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.178 (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 D_{-\frac {1}{2}-\frac {i}{2}}((-1+i) x)+(1+i) D_{\frac {1}{2}-\frac {i}{2}}((-1+i) x)-c_1 x D_{-\frac {1}{2}+\frac {i}{2}}((1+i) x)+(1-i) c_1 D_{\frac {1}{2}+\frac {i}{2}}((1+i) x)\right )}{D_{-\frac {1}{2}-\frac {i}{2}}((-1+i) x)+c_1 D_{-\frac {1}{2}+\frac {i}{2}}((1+i) x)} \\ y(x)\to \frac {(1+i) D_{\frac {1}{2}+\frac {i}{2}}((1+i) x)}{D_{-\frac {1}{2}+\frac {i}{2}}((1+i) x)}-i x \\ \end{align*}