29.35.26 problem 1060

Internal problem ID [5624]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1060
Date solved : Monday, January 27, 2025 at 12:29:40 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 36

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

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