1.27 problem 27

Internal problem ID [6590]

Book: First order enumerated odes
Section: section 1
Problem number: 27.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

Solve \begin {gather*} \boxed {y^{\prime }-\sin \relax (x )-y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 54

dsolve(diff(y(x),x)=sin(x)+y(x)^2,y(x), singsol=all)
 

\[ y \relax (x ) = -\frac {c_{1} \MathieuSPrime \left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )+\MathieuCPrime \left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )}{2 \left (c_{1} \MathieuS \left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )+\MathieuC \left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )\right )} \]

Solution by Mathematica

Time used: 0.296 (sec). Leaf size: 105

DSolve[y'[x]==Sin[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-\text {MathieuSPrime}\left [0,-2,\frac {1}{4} (\pi -2 x)\right ]+c_1 \text {MathieuCPrime}\left [0,-2,\frac {1}{4} (\pi -2 x)\right ]}{2 \left (\text {MathieuS}\left [0,-2,\frac {1}{4} (2 x-\pi )\right ]+c_1 \text {MathieuC}\left [0,-2,\frac {1}{4} (\pi -2 x)\right ]\right )} \\ y(x)\to \frac {\text {MathieuCPrime}\left [0,-2,\frac {1}{4} (\pi -2 x)\right ]}{2 \text {MathieuC}\left [0,-2,\frac {1}{4} (\pi -2 x)\right ]} \\ \end{align*}