82.13.3 problem Ex. 3

Internal problem ID [18803]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 32
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:18:37 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.698 (sec). Leaf size: 65

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

\begin{align*} y \left (x \right ) &= -x +c_{1} \\ y \left (x \right ) &= \frac {-c_{1} x -\sqrt {-3 x^{2} c_{1}^{2}+4}}{2 c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {-3 x^{2} c_{1}^{2}+4}}{2 c_{1}} \\ y \left (x \right ) &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.484 (sec). Leaf size: 130

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

\begin{align*} y(x)\to \frac {1}{2} \left (-x-\sqrt {-3 x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (-x+\sqrt {-3 x^2+4 e^{c_1}}\right ) \\ y(x)\to c_1 \\ y(x)\to -x+c_1 \\ y(x)\to \frac {1}{2} \left (-\sqrt {3} \sqrt {-x^2}-x\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {3} \sqrt {-x^2}-x\right ) \\ \end{align*}