Internal problem ID [13316]
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: 4.5 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-2 y x +y=2 x -1} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(x),x)=2*x-1+2*x*y(x)-y(x),y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -1+3 \,{\mathrm e}^{x \left (-1+x \right )} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 16
DSolve[{y'[x]==2*x-1+2*x*y[x]-y[x],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{(x-1) x}-1 \]