29.36.10 problem 1076

Internal problem ID [5637]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1076
Date solved : Monday, January 27, 2025 at 12:43:40 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 65

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

✓ Solution by Mathematica

Time used: 0.534 (sec). Leaf size: 130

DSolve[(x+2 y[x])(D[y[x],x])^3+3 (x+y[x]) (D[y[x],x])^2+ (2 x+y[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*}