60.1.325 problem 326

Internal problem ID [10339]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 326
Date solved : Monday, January 27, 2025 at 07:14:52 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.582 (sec). Leaf size: 160

dsolve(y(x)*((a*y(x)+b*x)^3+b*x^3)*diff(y(x),x)+x*((a*y(x)+b*x)^3+a*y(x)^3) = 0,y(x), singsol=all)
 

\[ y = \frac {x \left (c_{1} x -b \operatorname {RootOf}\left (b^{2} \textit {\_Z}^{4}-2 b x c_{1} \textit {\_Z}^{3}+\left (a^{2} c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c_{1}^{2} x^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_{1}^{3} \textit {\_Z} +c_{1}^{4} x^{4}\right )\right )}{a \operatorname {RootOf}\left (b^{2} \textit {\_Z}^{4}-2 b x c_{1} \textit {\_Z}^{3}+\left (a^{2} c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c_{1}^{2} x^{2}-a^{2}\right ) \textit {\_Z}^{2}-2 b \,x^{3} c_{1}^{3} \textit {\_Z} +c_{1}^{4} x^{4}\right )} \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 113

DSolve[x*(a*y[x]^3 + (b*x + a*y[x])^3) + y[x]*(b*x^3 + (b*x + a*y[x])^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1] \left (b^3+3 a K[1] b^2+3 a^2 K[1]^2 b+b+a^3 K[1]^3\right )}{(b+a K[1]) \left (a^2 K[1]^4+2 a b K[1]^3+a^2 K[1]^2+b^2 K[1]^2+K[1]^2+2 a b K[1]+b^2\right )}dK[1]=-\log (x)+c_1,y(x)\right ] \]