29.33.13 problem 975

Internal problem ID [5552]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 975
Date solved : Monday, January 27, 2025 at 11:46:18 AM
CAS classification : [_quadrature]

\begin{align*} y^{2} {y^{\prime }}^{2}-\left (1+x \right ) y y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 45

dsolve(y(x)^2*diff(y(x),x)^2-(1+x)*y(x)*diff(y(x),x)+x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 72

DSolve[y[x]^2 (D[y[x],x])^2-(1+x)y[x] D[y[x],x]+x==0,y[x],x,IncludeSingularSolutions -> True]
 

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