29.28.5 problem 802

Internal problem ID [5386]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 802
Date solved : Monday, January 27, 2025 at 11:17:41 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

\begin{align*} y \left (x \right ) &= \frac {2}{3} x^{3}-x^{2}+c_{1} \\ y \left (x \right ) &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 \\ y(x)\to \frac {2 x^3}{3}-x^2+c_1 \\ \end{align*}