29.30.16 problem 875

Internal problem ID [5456]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 875
Date solved : Monday, January 27, 2025 at 11:24:35 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 28

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

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