29.35.17 problem 1050

Internal problem ID [5615]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1050
Date solved : Monday, January 27, 2025 at 12:26:51 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 48

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

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