60.2.256 problem 832

Internal problem ID [10843]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 832
Date solved : Tuesday, January 28, 2025 at 05:24:11 PM
CAS classification : [_rational]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

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

\[ \ln \left (x +1\right )+\frac {x}{y}-\frac {y^{3}}{3}-\frac {y^{2}}{2}-y+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.362 (sec). Leaf size: 64

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

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