83.21.5 problem 5

Internal problem ID [19249]
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 : 5
Date solved : Tuesday, January 28, 2025 at 01:15:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.349 (sec). Leaf size: 22

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

\[ y \left (x \right ) = c_{1} x +\sqrt {-a^{2} c_{1}^{2}+b^{2}} \]

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 38

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

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