Internal problem ID [4258]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}-\frac {1}{x +\sqrt {x^{2}+1}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 19
dsolve(diff(y(x),x)+y(x)/sqrt(x^2+1)=1/(x+sqrt(x^2+1)),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}+x}{x +\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.323 (sec). Leaf size: 78
DSolve[y'[x]*y[x]/Sqrt[x^2+1]==1/(x+Sqrt[x^2+1]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\frac {2}{3}} \sqrt {x^3-\left (x^2+1\right )^{3/2}+3 x+3 c_1} \\ y(x)\to \sqrt {\frac {2}{3}} \sqrt {x^3-\left (x^2+1\right )^{3/2}+3 x+3 c_1} \\ \end{align*}