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]
Solve \begin {gather*} \boxed {\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.266 (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)
\[ y \relax (x ) = \frac {\left (260-108 x^{2}-108 \sin \relax (x )+12 \sqrt {81 x^{4}+162 x^{2} \sin \relax (x )-81 \left (\cos ^{2}\relax (x )\right )-390 x^{2}-390 \sin \relax (x )+522}\right )^{\frac {1}{3}}}{6}+\frac {8}{3 \left (260-108 x^{2}-108 \sin \relax (x )+12 \sqrt {81 x^{4}+162 x^{2} \sin \relax (x )-81 \left (\cos ^{2}\relax (x )\right )-390 x^{2}-390 \sin \relax (x )+522}\right )^{\frac {1}{3}}}-\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 2.605 (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*}