29.8.5 problem 210

Internal problem ID [4810]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 210
Date solved : Monday, January 27, 2025 at 09:40:34 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime }+x +\tan \left (x +y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.875 (sec). Leaf size: 117

dsolve(x*diff(y(x),x)+x+tan(x+y(x)) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.879 (sec). Leaf size: 16

DSolve[x D[y[x],x]+x+Tan[x+y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+\arcsin \left (\frac {c_1}{x}\right ) \]