60.2.357 problem 934

Internal problem ID [10944]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 934
Date solved : Monday, January 27, 2025 at 10:29:34 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 39

dsolve(diff(y(x),x) = 1/2*x+1+y(x)^2+1/4*x^2*y(x)-x*y(x)-1/8*x^4+1/8*x^3+1/4*x^2+y(x)^3-3/4*x^2*y(x)^2-3/2*x*y(x)^2+3/16*y(x)*x^4+3/4*x^3*y(x)-1/64*x^6-3/32*x^5,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 71

DSolve[D[y[x],x] == 1 + x/2 + x^2/4 + x^3/8 - x^4/8 - (3*x^5)/32 - x^6/64 - x*y[x] + (x^2*y[x])/4 + (3*x^3*y[x])/4 + (3*x^4*y[x])/16 + y[x]^2 - (3*x*y[x]^2)/2 - (3*x^2*y[x]^2)/4 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\sqrt [3]{\frac {2}{31}} \left (\frac {1}{4} \left (-3 x^2-6 x+4\right )+3 y(x)\right )}\frac {1}{K[1]^3-3 \left (\frac {2}{31}\right )^{2/3} K[1]+1}dK[1]=\frac {1}{9} \left (\frac {31}{2}\right )^{2/3} x+c_1,y(x)\right ] \]