60.2.121 problem 697

Internal problem ID [10708]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 697
Date solved : Monday, January 27, 2025 at 09:28:46 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 38

dsolve(diff(y(x),x) = (1+y(x)^2*exp(-4/3*x)+y(x)^3*exp(-2*x))*exp(2/3*x),y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (-x +3 \left (\int _{}^{\textit {\_Z}}\frac {1}{3 \textit {\_a}^{3}+3 \textit {\_a}^{2}-2 \textit {\_a} +3}d \textit {\_a} \right )+c_{1} \right ) {\mathrm e}^{\frac {2 x}{3}} \]

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 90

DSolve[D[y[x],x] == E^((2*x)/3)*(1 + y[x]^2/E^((4*x)/3) + y[x]^3/E^(2*x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 e^{-4 x/3} y(x)+e^{-2 x/3}}{\sqrt [3]{35} \sqrt [3]{e^{-2 x}}}}\frac {1}{K[1]^3-\frac {9 K[1]}{35^{2/3}}+1}dK[1]=\frac {1}{9} 35^{2/3} e^{4 x/3} \left (e^{-2 x}\right )^{2/3} x+c_1,y(x)\right ] \]