Internal problem ID [12977]
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: 0.0 (sec). Leaf size: 47
dsolve(diff(y(x),x)+(8-x)*y(x)-y(x)^2=-8*x,y(x), singsol=all)
\[ y = 8+\frac {{\mathrm e}^{\frac {1}{2} x^{2}+8 x}}{c_{1} +\frac {i \sqrt {\pi }\, {\mathrm e}^{-32} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}+4 i \sqrt {2}\right )}{2}} \]
✓ 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*}