12.3.12 problem 13

Internal problem ID [1589]
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 : 13
Date solved : Monday, January 27, 2025 at 05:09:38 AM
CAS classification : [_separable]

\begin{align*} \left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.374 (sec). Leaf size: 102

dsolve([(3*y(x)^2+4*y(x))*diff(y(x),x)+2*x+cos(x)=0,y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (260-108 x^{2}-108 \sin \left (x \right )+12 \sqrt {441-390 x^{2}-390 \sin \left (x \right )+81 x^{4}+162 \sin \left (x \right ) x^{2}+81 \sin \left (x \right )^{2}}\right )^{{1}/{3}}}{6}+\frac {8}{3 \left (260-108 x^{2}-108 \sin \left (x \right )+12 \sqrt {441-390 x^{2}-390 \sin \left (x \right )+81 x^{4}+162 \sin \left (x \right ) x^{2}+81 \sin \left (x \right )^{2}}\right )^{{1}/{3}}}-\frac {2}{3} \]

✓ Solution by Mathematica

Time used: 2.426 (sec). Leaf size: 127

DSolve[{(3*y[x]^2+4*y[x])*D[y[x],x]+2*x+Cos[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2^{2/3} \left (-27 x^2+\sqrt {\left (27 x^2+27 \sin (x)-65\right )^2-256}-27 \sin (x)+65\right )^{2/3}-4 \sqrt [3]{-27 x^2+\sqrt {\left (27 x^2+27 \sin (x)-65\right )^2-256}-27 \sin (x)+65}+8 \sqrt [3]{2}}{6 \sqrt [3]{-27 x^2+\sqrt {\left (27 x^2+27 \sin (x)-65\right )^2-256}-27 \sin (x)+65}} \]