Internal problem ID [15092]
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.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
\[ \boxed {{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 87
dsolve(diff(y(x),x)^3+(x+2)*exp(y(x))=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 3 \ln \left (12\right )-3 \ln \left (\left (6+3 x \right ) \left (2+x \right )^{\frac {1}{3}}+4 c_{1} \right ) \\ y \left (x \right ) &= 3 \ln \left (24\right )-3 \ln \left (-3 \left (1+i \sqrt {3}\right ) \left (2+x \right )^{\frac {4}{3}}+8 c_{1} \right ) \\ y \left (x \right ) &= 3 \ln \left (24\right )-3 \ln \left (3 \left (i \sqrt {3}-1\right ) \left (2+x \right )^{\frac {4}{3}}+8 c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.699 (sec). Leaf size: 126
DSolve[y'[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*}