Internal problem ID [15162]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 300.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-{\mathrm e}^{x +2 y}=1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 30
dsolve(diff(y(x),x)-1=exp(x+2*y(x)),y(x), singsol=all)
\[ y = -\frac {x}{2}+\frac {\ln \left (3\right )}{2}+\frac {\ln \left (\frac {{\mathrm e}^{3 x}}{-2 \,{\mathrm e}^{3 x}+c_{1}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.931 (sec). Leaf size: 26
DSolve[y'[x]-1==Exp[x+2*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x-\frac {1}{2} \log \left (-\frac {2}{3} \left (e^{3 x}+3 c_1\right )\right ) \]