29.31.5 problem 904

Internal problem ID [5484]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 904
Date solved : Monday, January 27, 2025 at 11:27:18 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.163 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 1.905 (sec). Leaf size: 58

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

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