Internal problem ID [2712]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 67.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}}=\frac {1}{2 \sqrt {x +1}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(sec(y(x))^2*diff(y(x),x)+1/(2*sqrt(1+x))*tan(y(x))=1/(2*sqrt(1+x)),y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left ({\mathrm e}^{-\sqrt {x +1}} c_{1} +1\right ) \]
✓ Solution by Mathematica
Time used: 60.288 (sec). Leaf size: 247
DSolve[Sec[y[x]]^2*y'[x]+1/(2*Sqrt[1+x])*Tan[y[x]]==1/(2*Sqrt[1+x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {e^{\sqrt {x+1}+2 c_1}}{\sqrt {-2 e^{\sqrt {x+1}+2 c_1}+2 e^{2 \sqrt {x+1}+4 c_1}+1}}\right ) y(x)\to \arccos \left (-\frac {e^{\sqrt {x+1}+2 c_1}}{\sqrt {-2 e^{\sqrt {x+1}+2 c_1}+2 e^{2 \sqrt {x+1}+4 c_1}+1}}\right ) y(x)\to -\arccos \left (\frac {e^{\sqrt {x+1}+2 c_1}}{\sqrt {-2 e^{\sqrt {x+1}+2 c_1}+2 e^{2 \sqrt {x+1}+4 c_1}+1}}\right ) y(x)\to \arccos \left (\frac {e^{\sqrt {x+1}+2 c_1}}{\sqrt {-2 e^{\sqrt {x+1}+2 c_1}+2 e^{2 \sqrt {x+1}+4 c_1}+1}}\right ) \end{align*}