Internal problem ID [939]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.5 (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)
\[ y \left (x \right ) = \frac {\left (260-108 x^{2}-108 \sin \left (x \right )+12 \sqrt {441-390 x^{2}-390 \sin \left (x \right )+81 x^{4}+162 \sin \left (x \right ) x^{2}+81 \sin \left (x \right )^{2}}\right )^{\frac {1}{3}}}{6}+\frac {8}{3 \left (260-108 x^{2}-108 \sin \left (x \right )+12 \sqrt {441-390 x^{2}-390 \sin \left (x \right )+81 x^{4}+162 \sin \left (x \right ) x^{2}+81 \sin \left (x \right )^{2}}\right )^{\frac {1}{3}}}-\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 2.384 (sec). Leaf size: 114
DSolve[{(3*y[x]^2+4*y[x])*y'[x]+2*x+Cos[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (2^{2/3} \sqrt [3]{-27 x^2+3 \sqrt {3} \sqrt {\left (x^2+\sin (x)-3\right ) \left (27 x^2+27 \sin (x)-49\right )}-27 \sin (x)+65}+\frac {8 \sqrt [3]{2}}{\sqrt [3]{-27 x^2+3 \sqrt {3} \sqrt {\left (x^2+\sin (x)-3\right ) \left (27 x^2+27 \sin (x)-49\right )}-27 \sin (x)+65}}-4\right ) \\ \end{align*}