60.2.8 problem 584

Internal problem ID [10595]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 584
Date solved : Monday, January 27, 2025 at 09:17:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 35

dsolve(diff(y(x),x) = 2*a/(y(x)+2*F(y(x)^2-4*a*x)*a),y(x), singsol=all)
 

\[ \frac {y}{2 a}+\frac {\int _{}^{-4 a x +y^{2}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a}}{8 a^{2}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 115

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{4 a^2 F\left (K[2]^2-4 a x\right )}-\frac {2 a \int _1^x\frac {K[2] F''\left (K[2]^2-4 a K[1]\right )}{a F\left (K[2]^2-4 a K[1]\right )^2}dK[1]-1}{2 a}\right )dK[2]+\int _1^x-\frac {1}{2 a F\left (y(x)^2-4 a K[1]\right )}dK[1]=c_1,y(x)\right ] \]