Internal problem ID [4464]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \sqrt {1+\sin ^{2}\relax (x )}-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.925 (sec). Leaf size: 48
dsolve([diff(y(x),x)+y(x)*sqrt(1+sin(x)^2)=x,y(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \left (\int _{0}^{x}\textit {\_z1} \,{\mathrm e}^{-\EllipticE \left (\cos \left (\textit {\_z1} \right ), \frac {\sqrt {2}}{2}\right ) \sqrt {2}\, \mathrm {csgn}\left (\sin \left (\textit {\_z1} \right )\right )}d \textit {\_z1} +2\right ) {\mathrm e}^{\mathrm {csgn}\left (\sin \relax (x )\right ) \EllipticE \left (\cos \relax (x ), \frac {\sqrt {2}}{2}\right ) \sqrt {2}} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 31
DSolve[{y'[x]+y[x]*Sqrt[1+Sin[x]^2]==x,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-E(x|-1)} \left (\int _0^xe^{E(K[1]|-1)} K[1]dK[1]+2\right ) \\ \end{align*}