Internal problem ID [13306]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.3 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y x +2 y=-3 x +6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)=x*y(x)-3*x-2*y(x)+6,y(x), singsol=all)
\[ y \left (x \right ) = 3+{\mathrm e}^{\frac {\left (x -4\right ) x}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 25
DSolve[y'[x]==x*y[x]-3*x-2*y[x]+6,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3+c_1 e^{\frac {1}{2} (x-4) x} \\ y(x)\to 3 \\ \end{align*}