73.2.10 problem 3.4 j

Internal problem ID [15033]
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
Date solved : Tuesday, January 28, 2025 at 07:28:06 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+\left (8-x \right ) y-y^{2}&=-8 x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 62

dsolve(diff(y(x),x)+(8-x)*y(x)-y(x)^2=-8*x,y(x), singsol=all)
 

\[ y = \frac {8 i \sqrt {\pi }\, {\mathrm e}^{-32} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +8\right )}{2}\right )+2 \,{\mathrm e}^{\frac {x \left (16+x \right )}{2}}+16 c_{1}}{i \sqrt {\pi }\, {\mathrm e}^{-32} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +8\right )}{2}\right )+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.357 (sec). Leaf size: 88

DSolve[D[y[x],x]+(8-x)*y[x]-y[x]^2==-8*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 8+\frac {e^{\frac {1}{2} x (x+16)}}{-\int _1^xe^{\frac {1}{2} K[1] (K[1]+16)}dK[1]+c_1} \\ y(x)\to 8 \\ y(x)\to 8-\frac {e^{\frac {1}{2} x (x+16)}}{\int _1^xe^{\frac {1}{2} K[1] (K[1]+16)}dK[1]} \\ \end{align*}