Internal problem ID [13302]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.3 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\sqrt {x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)=sqrt(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \sqrt {x^{2}+1}}{2}+\frac {\operatorname {arcsinh}\left (x \right )}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 40
DSolve[y'[x]==Sqrt[1+x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {x^2+1} x-\frac {1}{2} \log \left (\sqrt {x^2+1}-x\right )+c_1 \]