60.2.371 problem 948

Internal problem ID [10958]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 948
Date solved : Monday, January 27, 2025 at 10:32:00 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 x y^{4}+4 y^{8}+12 y^{7}+33 y^{6}} \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 68

dsolve(diff(y(x),x) = -216*y(x)/(-216*y(x)^4-252*y(x)^3-396*y(x)^2-216*y(x)+36*x^2-72*x*y(x)+60*y(x)^5-36*x*y(x)^3-72*x*y(x)^2-24*x*y(x)^4+4*y(x)^8+12*y(x)^7+33*y(x)^6),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (12 c_{1} {\mathrm e}^{4 \textit {\_Z}}+2 \,{\mathrm e}^{4 \textit {\_Z}} \textit {\_Z} +18 \,{\mathrm e}^{3 \textit {\_Z}} c_{1} +3 \,{\mathrm e}^{3 \textit {\_Z}} \textit {\_Z} +36 c_{1} {\mathrm e}^{2 \textit {\_Z}}+6 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}+36 c_{1} {\mathrm e}^{\textit {\_Z}}+6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-36 c_{1} x -6 x \textit {\_Z} +36\right )} \]

✓ Solution by Mathematica

Time used: 0.452 (sec). Leaf size: 39

DSolve[D[y[x],x] == (-216*y[x])/(36*x^2 - 216*y[x] - 72*x*y[x] - 396*y[x]^2 - 72*x*y[x]^2 - 252*y[x]^3 - 36*x*y[x]^3 - 216*y[x]^4 - 24*x*y[x]^4 + 60*y[x]^5 + 33*y[x]^6 + 12*y[x]^7 + 4*y[x]^8),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {36}{y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x}+\log (y(x))=c_1,y(x)\right ] \]