29.32.1 problem 935

Internal problem ID [5513]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 935
Date solved : Monday, January 27, 2025 at 11:34:49 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.134 (sec). Leaf size: 129

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

\begin{align*} y \left (x \right ) &= -4 x^{2} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (\sqrt {2}\, c_{1} -2 x \right ) x \,c_{1}^{2}}{2 c_{1}^{2}-4 x^{2}} \\ y \left (x \right ) &= -\frac {\left (\sqrt {2}\, c_{1} +2 x \right ) x \,c_{1}^{2}}{2 c_{1}^{2}-4 x^{2}} \\ y \left (x \right ) &= -\frac {2 \left (-c_{1} x +\sqrt {2}\right ) x}{c_{1} \left (c_{1}^{2} x^{2}-2\right )} \\ y \left (x \right ) &= \frac {2 \left (c_{1} x +\sqrt {2}\right ) x}{c_{1} \left (c_{1}^{2} x^{2}-2\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.780 (sec). Leaf size: 79

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

\begin{align*} y(x)\to -\frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{x+i \cosh (c_1)+i \sinh (c_1)} \\ y(x)\to \frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{-x+i \cosh (c_1)+i \sinh (c_1)} \\ y(x)\to 0 \\ \end{align*}