30.1.9 problem example page 47

Internal problem ID [5697]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : example page 47
Date solved : Monday, January 27, 2025 at 01:07:37 PM
CAS classification : [_Clairaut]

\begin{align*} y&=x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \end{align*}

✓ Solution by Maple

Time used: 1.864 (sec). Leaf size: 17

dsolve(y(x)=x*diff(y(x),x)+ a*diff(y(x),x)/(sqrt(1+diff(y(x),x)^2)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 35.870 (sec). Leaf size: 27

DSolve[y[x]==x*D[y[x],x]+ a*D[y[x],x]/(Sqrt[1+(D[y[x],x])^2]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x+\frac {a}{\sqrt {1+c_1{}^2}}\right ) \\ y(x)\to 0 \\ \end{align*}