28.1.39 problem 39

Internal problem ID [4345]
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
Date solved : Monday, January 27, 2025 at 09:06:19 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} 2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

dsolve(2*x*(x^2-sin(y(x))+1)+(x^2+1)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\arcsin \left (\left (x^{2}+1\right ) \left (\ln \left (x^{2}+1\right )+c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 7.272 (sec). Leaf size: 25

DSolve[2*x*(x^2-Sin[y[x]]+1)+(x^2+1)*Cos[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\arcsin \left (\left (x^2+1\right ) \left (\log \left (x^2+1\right )+8 c_1\right )\right ) \]