Internal problem ID [2958]
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]]
Solve \begin {gather*} \boxed {y^{\prime } x +x +\tan \left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.038 (sec). Leaf size: 166
dsolve(x*diff(y(x),x)+x+tan(x+y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arctan \left (\frac {\sin \relax (x ) \cos \relax (x ) c_{1} x^{2}+\sqrt {\left (\sin ^{4}\relax (x )\right ) c_{1}^{2} x^{4}+\left (\sin ^{2}\relax (x )\right ) \left (\cos ^{2}\relax (x )\right ) c_{1}^{2} x^{4}-\left (\sin ^{2}\relax (x )\right ) c_{1}^{2} x^{4}+c_{1} x^{2}-1}}{\left (\sin ^{2}\relax (x )\right ) c_{1} x^{2}-c_{1} x^{2}+1}\right ) \\ y \relax (x ) = -\arctan \left (\frac {-\sin \relax (x ) \cos \relax (x ) c_{1} x^{2}+\sqrt {\left (\sin ^{4}\relax (x )\right ) c_{1}^{2} x^{4}+\left (\sin ^{2}\relax (x )\right ) \left (\cos ^{2}\relax (x )\right ) c_{1}^{2} x^{4}-\left (\sin ^{2}\relax (x )\right ) c_{1}^{2} x^{4}+c_{1} x^{2}-1}}{\left (\sin ^{2}\relax (x )\right ) c_{1} x^{2}-c_{1} x^{2}+1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.299 (sec). Leaf size: 16
DSolve[x y'[x]+x+Tan[x+y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\text {ArcSin}\left (\frac {c_1}{x}\right ) \\ \end{align*}