57.1.27 problem 27

Internal problem ID [9011]
Book : First order enumerated odes
Section : section 1
Problem number : 27
Date solved : Monday, January 27, 2025 at 05:27:12 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 105

DSolve[D[y[x],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*}