36.2.23 problem 27

Internal problem ID [6316]
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
Date solved : Monday, January 27, 2025 at 01:56:01 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}}&=x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.596 (sec). Leaf size: 34

dsolve([diff(y(x),x)+y(x)*sqrt(1+sin(x)^2)=x,y(0) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {csgn}\left (\cos \left (x \right )\right ) \operatorname {EllipticE}\left (\sin \left (x \right ), i\right )} \left (\int _{0}^{x}\textit {\_z1} \,{\mathrm e}^{\operatorname {csgn}\left (\cos \left (\textit {\_z1} \right )\right ) \operatorname {EllipticE}\left (\sin \left (\textit {\_z1} \right ), i\right )}d \textit {\_z1} +2\right ) \]

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 31

DSolve[{D[y[x],x]+y[x]*Sqrt[1+Sin[x]^2]==x,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-E(x|-1)} \left (\int _0^xe^{E(K[1]|-1)} K[1]dK[1]+2\right ) \]