Internal problem ID [496]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-{\mathrm e}^{x}+{\mathrm e}^{-x}}{3+4 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 29
dsolve([diff(y(x),x) = (exp(-x)-exp(x))/(3+4*y(x)),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3}{4}+\frac {\sqrt {{\mathrm e}^{x} \left (-8 \,{\mathrm e}^{2 x}+65 \,{\mathrm e}^{x}-8\right )}\, {\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 21
DSolve[{y'[x] == (Exp[-x]-Exp[x])/(3+4*y[x]),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\sqrt {65-16 \cosh (x)}-3\right ) \\ \end{align*}