12.3.4 problem 5

Internal problem ID [1581]
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
Date solved : Monday, January 27, 2025 at 05:09:12 AM
CAS classification : [_separable]

\begin{align*} \left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ \ln \left (x^{2}+1\right )+\arctan \left (x \right )+y^{3}+3 \sin \left (y\right )+\ln \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.351 (sec). Leaf size: 40

DSolve[(3*y[x]^3+3*y[x]*Cos[y[x]]+1)*D[y[x],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 [-\arctan (x)-\log \left (x^2+1\right )+c_1\right ] \\ y(x)\to 0 \\ \end{align*}