73.4.5 problem 5.1 (e)

Internal problem ID [15087]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (e)
Date solved : Tuesday, January 28, 2025 at 07:30:18 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+y x +3 y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

dsolve(diff(y(x),x)=1+x*y(x)+3*y(x),y(x), singsol=all)
 

\[ y = \frac {\left (\sqrt {\pi }\, {\mathrm e}^{\frac {9}{2}} \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +3\right )}{2}\right )+2 c_{1} \right ) {\mathrm e}^{\frac {x \left (6+x \right )}{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 38

DSolve[D[y[x],x]==1+x*y[x]+3*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {1}{2} x (x+6)} \left (\int _1^xe^{-\frac {1}{2} K[1] (K[1]+6)}dK[1]+c_1\right ) \]