60.1.523 problem 526

Internal problem ID [10537]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 526
Date solved : Monday, January 27, 2025 at 08:52:15 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}-\left (y^{2}+y x +x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 32

dsolve(diff(y(x),x)^3-(y(x)^2+x*y(x)+x^2)*diff(y(x),x)^2+(x*y(x)^3+x^2*y(x)^2+x^3*y(x))*diff(y(x),x)-x^3*y(x)^3=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{3}}{3}+c_{1} \\ y &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y &= \frac {1}{-x +c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 48

DSolve[-(x^3*y[x]^3) + (x^3*y[x] + x^2*y[x]^2 + x*y[x]^3)*D[y[x],x] - (x^2 + x*y[x] + y[x]^2)*D[y[x],x]^2 + D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{x+c_1} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to \frac {x^3}{3}+c_1 \\ y(x)\to 0 \\ \end{align*}