83.21.7 problem 7

Internal problem ID [19251]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:15:42 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 53

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

\begin{align*} y(x)\to \frac {a}{c_1}+c_1 x \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {a} \sqrt {x} \\ y(x)\to 2 \sqrt {a} \sqrt {x} \\ \end{align*}