Internal problem ID [3466]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 210.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime }+\tan \left (y+x \right )=-x} \]
✓ Solution by Maple
Time used: 0.266 (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: 4.917 (sec). Leaf size: 16
DSolve[x y'[x]+x+Tan[x+y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x+\arcsin \left (\frac {c_1}{x}\right ) \]