60.2.359 problem 936

Internal problem ID [10946]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 936
Date solved : Monday, January 27, 2025 at 10:29:39 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 y x^{4}}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 39

dsolve(diff(y(x),x) = -1/4*x+1+y(x)^2+7/16*x^2*y(x)-1/2*x*y(x)+5/128*x^4-5/64*x^3+1/16*x^2+y(x)^3+3/8*x^2*y(x)^2-3/4*x*y(x)^2+3/64*y(x)*x^4-3/16*x^3*y(x)+1/512*x^6-3/256*x^5,y(x), singsol=all)
 

\[ y = -\frac {x^{2}}{8}+\frac {x}{4}+\operatorname {RootOf}\left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {1}{4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+3}d \textit {\_a} \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 80

DSolve[D[y[x],x] == 1 - x/4 + x^2/16 - (5*x^3)/64 + (5*x^4)/128 - (3*x^5)/256 + x^6/512 - (x*y[x])/2 + (7*x^2*y[x])/16 - (3*x^3*y[x])/16 + (3*x^4*y[x])/64 + y[x]^2 - (3*x*y[x]^2)/4 + (3*x^2*y[x]^2)/8 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {2^{2/3} \left (\frac {1}{8} \left (3 x^2-6 x+8\right )+3 y(x)\right )}{\sqrt [3]{89}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{2} K[1]}{89^{2/3}}+1}dK[1]=\frac {89^{2/3} x}{18 \sqrt [3]{2}}+c_1,y(x)\right ] \]