Internal problem ID [14998]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 91.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\tan \left (y^{\prime }\right )=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(tan(diff(y(x),x))=x,y(x), singsol=all)
\[ y = x \arctan \left (x \right )-\frac {\ln \left (x^{2}+1\right )}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 163
DSolve[Tan[y'[x]]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2} \log \left (x^2+1\right )}{2 x}-x \cos ^{-1}\left (-\frac {1}{\sqrt {x^2+1}}\right )+c_1 \\ y(x)\to -\frac {\sqrt {x^2} \log \left (x^2+1\right )}{2 x}+x \cos ^{-1}\left (\frac {1}{\sqrt {x^2+1}}\right )+c_1 \\ y(x)\to \frac {\sqrt {x^2} \log \left (x^2+1\right )}{2 x}+x \cos ^{-1}\left (-\frac {1}{\sqrt {x^2+1}}\right )+c_1 \\ y(x)\to \frac {\sqrt {x^2} \log \left (x^2+1\right )}{2 x}-x \cos ^{-1}\left (\frac {1}{\sqrt {x^2+1}}\right )+c_1 \\ \end{align*}