Internal problem ID [48]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-2 y=-1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([1+diff(y(x),x) = 2*y(x),y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{2}+\frac {{\mathrm e}^{2 x -2}}{2} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 18
DSolve[{1+y'[x] == 2*y[x],y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (e^{2 x-2}+1\right ) \]