Internal problem ID [3312]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+\left (\sin \left (x \right )-y\right ) y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x) = cos(x)-(sin(x)-y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-\cos \left (x \right )}}{c_{1} +\int {\mathrm e}^{-\cos \left (x \right )}d x}+\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 42.807 (sec). Leaf size: 158
DSolve[y'[x]==Cos[x]-(Sin[x]-y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \sin (x) \int _1^xe^{-\cos (K[1])}dK[1]+\sin (x)+c_1 \left (-e^{-\cos (x)}\right )}{1+c_1 \int _1^xe^{-\cos (K[1])}dK[1]} y(x)\to \sin (x) y(x)\to \frac {\sin ^3(x) e^{\cos (x)} \int _1^{\cos (x)}\frac {e^{-K[1]} K[1]}{\left (1-K[1]^2\right )^{3/2}}dK[1]}{\sin ^2(x) e^{\cos (x)} \int _1^{\cos (x)}\frac {e^{-K[1]} K[1]}{\left (1-K[1]^2\right )^{3/2}}dK[1]-\sqrt {\sin ^2(x)}} \end{align*}