Internal problem ID [13351]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y x -3 y=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x)=1+x*y(x)+3*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\sqrt {\pi }\, {\mathrm e}^{\frac {9}{2}} \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +3\right )}{2}\right )+2 c_{1} \right ) {\mathrm e}^{\frac {x \left (x +6\right )}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 47
DSolve[y'[x]==1+x*y[x]+3*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{\frac {1}{2} x (x+6)} \left (e^{9/2} \sqrt {2 \pi } \text {erf}\left (\frac {x+3}{\sqrt {2}}\right )+2 c_1\right ) \]