29.29.5 problem 827

Internal problem ID [5410]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 827
Date solved : Monday, January 27, 2025 at 11:21:20 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 48

dsolve(diff(y(x),x)^2+2*x*y(x)^3*diff(y(x),x)+y(x)^4 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {1}{x} \\ y \left (x \right ) &= \frac {1}{x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {1}{\sqrt {-c_{1} \left (c_{1} -2 x \right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} \left (2 x -c_{1} \right )}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.720 (sec). Leaf size: 171

DSolve[(D[y[x],x])^2+2 x y[x]^3 D[y[x],x]+y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {Solve}\left [-\frac {\sqrt {1-x^2 y(x)^2} y(x)^3 \text {arcsinh}\left (x \sqrt {-y(x)^2}\right )}{\sqrt {-y(x)^2} \sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )}}-\log (y(x))&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {y(x)^3 \sqrt {1-x^2 y(x)^2} \text {arcsinh}\left (x \sqrt {-y(x)^2}\right )}{\sqrt {-y(x)^2} \sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )}}-\log (y(x))&=c_1,y(x)\right ] \\ y(x)\to 0 \\ y(x)\to -\frac {1}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}