62.17.2 problem Ex 2

Internal problem ID [12902]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:40:52 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.186 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 59

DSolve[y[x]*D[y[x],x]==(x-b)*(D[y[x],x])^2+a,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*}