Internal problem ID [3825]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1140.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (1+\left (y^{\prime }\right )^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 30
dsolve((1+diff(y(x),x)^2)*(arctan(diff(y(x),x))+a*x)+diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \int \tan \left (\RootOf \left (a x \left (\tan ^{2}\left (\textit {\_Z} \right )\right )+\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \textit {\_Z} +a x +\tan \left (\textit {\_Z} \right )+\textit {\_Z} \right )\right )d x +c_{1} \]
✓ Solution by Mathematica
Time used: 1.201 (sec). Leaf size: 58
DSolve[(1+(y'[x])^2)(ArcTan[y'[x]]+a x)+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{y(x)=\frac {1}{a \left (K[1]^2+1\right )}+c_1,x=\frac {K[1]^2 (-\text {ArcTan}(K[1]))-\text {ArcTan}(K[1])-K[1]}{a \left (K[1]^2+1\right )}\right \},\{y(x),K[1]\}\right ] \]