48.4.21 problem Problem 3.34

Internal problem ID [7563]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.34
Date solved : Tuesday, January 28, 2025 at 03:16:33 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 27

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

\[ y-\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]