Internal problem ID [13297]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 3. Some basics about First order equations. Additional exercises. page
63
Problem number: 3.4 j.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+\left (8-x \right ) y-y^{2}=-8 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
dsolve(diff(y(x),x)+(8-x)*y(x)-y(x)^2=-8*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {8 i \sqrt {\pi }\, {\mathrm e}^{-32} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +8\right )}{2}\right )+2 \,{\mathrm e}^{\frac {x \left (x +16\right )}{2}}+16 c_{1}}{i \sqrt {\pi }\, {\mathrm e}^{-32} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +8\right )}{2}\right )+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 54
DSolve[y'[x]+(8-x)*y[x]-y[x]^2==-8*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 8+\frac {2 e^{\frac {1}{2} (x+8)^2}}{-\sqrt {2 \pi } \text {erfi}\left (\frac {x+8}{\sqrt {2}}\right )+2 e^{32} c_1} \\ y(x)\to 8 \\ \end{align*}