Internal problem ID [52]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-6 \,{\mathrm e}^{2 x -y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([diff(y(x),x) = 6*exp(2*x-y(x)),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-2+3 \,{\mathrm e}^{2 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.739 (sec). Leaf size: 15
DSolve[{y'[x] == 6*Exp[2*x-y[x]],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (3 e^{2 x}-2\right ) \]