83.21.8 problem 8

Internal problem ID [19252]
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 : 8
Date solved : Tuesday, January 28, 2025 at 01:15:42 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 49

dsolve(y(x)=diff(y(x),x)*(x-b)+a/diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 59

DSolve[y[x]==D[y[x],x]*(x-b)+a/D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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