75.8.6 problem 204

Internal problem ID [16822]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 204
Date solved : Tuesday, January 28, 2025 at 09:33:54 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} {y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 2.181 (sec). Leaf size: 85

dsolve(diff(y(x),x)^3+(x+2)*exp(y(x))=0,y(x), singsol=all)
 

\begin{align*} y &= 3 \ln \left (12\right )-3 \ln \left (\left (3 x +6\right ) \left (x +2\right )^{{1}/{3}}+4 c_{1} \right ) \\ y &= 3 \ln \left (24\right )-3 \ln \left (-3 \left (1+i \sqrt {3}\right ) \left (x +2\right )^{{4}/{3}}+8 c_{1} \right ) \\ y &= 3 \ln \left (24\right )-3 \ln \left (3 \left (i \sqrt {3}-1\right ) \left (x +2\right )^{{4}/{3}}+8 c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.661 (sec). Leaf size: 126

DSolve[D[y[x],x]^3+(x+2)*Exp[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -3 \log \left (\frac {1}{12} \left (3 \sqrt [3]{x+2} x+6 \sqrt [3]{x+2}-4 c_1\right )\right ) \\ y(x)\to -3 \log \left (\frac {1}{12} \left (-3 \sqrt [3]{-1} \sqrt [3]{x+2} x-6 \sqrt [3]{-1} \sqrt [3]{x+2}-4 c_1\right )\right ) \\ y(x)\to -3 \log \left (\frac {1}{12} \left (3 (-1)^{2/3} \sqrt [3]{x+2} x+6 (-1)^{2/3} \sqrt [3]{x+2}-4 c_1\right )\right ) \\ \end{align*}