Internal problem ID [2675]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {2 x \left (x^{2}-\sin \relax (y)+1\right )+\left (x^{2}+1\right ) \cos \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 30
dsolve(2*x*(x^2-sin(y(x))+1)+(x^2+1)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\arcsin \left (\ln \left (x^{2}+1\right ) x^{2}+c_{1} x^{2}+\ln \left (x^{2}+1\right )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 3.544 (sec). Leaf size: 25
DSolve[2*x*(x^2-Sin[y[x]]+1)+(x^2+1)*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcSin}\left (\left (x^2+1\right ) \left (\log \left (x^2+1\right )+8 c_1\right )\right ) \\ \end{align*}