Internal problem ID [931]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (3 y^{3}+3 y \cos \relax (y)+1\right ) y^{\prime }+\frac {\left (1+2 x \right ) y}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 25
dsolve((3*y(x)^3+3*y(x)*cos(y(x))+1)*diff(y(x),x)+((2*x+1)*y(x))/(1+x^2)= 0,y(x), singsol=all)
\[ \ln \left (x^{2}+1\right )+\arctan \relax (x )+y \relax (x )^{3}+3 \sin \left (y \relax (x )\right )+\ln \left (y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.369 (sec). Leaf size: 40
DSolve[(3*y[x]^3+3*y[x]*Cos[y[x]]+1)*y'[x]+((2*x+1)*y[x])/(1+x^2)== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\text {$\#$1}^3+\log (\text {$\#$1})+3 \sin (\text {$\#$1})\&\right ]\left [-\text {ArcTan}(x)-\log \left (x^2+1\right )+c_1\right ] \\ y(x)\to 0 \\ \end{align*}