75.12.26 problem 300

Internal problem ID [16892]
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
Date solved : Tuesday, January 28, 2025 at 09:39:56 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }-1&={\mathrm e}^{x +2 y} \end{align*}

✓ Solution by Maple

Time used: 0.224 (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: 1.220 (sec). Leaf size: 26

DSolve[D[y[x],x]-1==Exp[x+2*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x-\frac {1}{2} \log \left (-\frac {2}{3} \left (e^{3 x}+3 c_1\right )\right ) \]