83.18.13 problem 13

Internal problem ID [19223]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:14:10 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 42

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

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