60.2.275 problem 851

Internal problem ID [10862]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 851
Date solved : Monday, January 27, 2025 at 10:17:47 PM
CAS classification : [[_homogeneous, `class C`], _Abel]

\begin{align*} y^{\prime }&=\frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +x^{2} b \,a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 42

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

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

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 92

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

\[ \text {Solve}\left [\int _1^{\frac {\frac {b+3 a x}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}}\frac {1}{K[1]^3-\frac {3 b^{2/3} K[1]}{(27 a+29 b)^{2/3}}+1}dK[1]=\frac {1}{9} x \left (\frac {27 a+29 b}{b}\right )^{2/3}+c_1,y(x)\right ] \]