Internal problem ID [495]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 21
dsolve([diff(y(x),x) = (-exp(x)+3*x^2)/(-5+2*y(x)),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {5}{2}-\frac {\sqrt {13+4 x^{3}-4 \,{\mathrm e}^{x}}}{2} \]
✓ Solution by Mathematica
Time used: 0.893 (sec). Leaf size: 29
DSolve[{y'[x] == (-Exp[x]+3*x^2)/(-5+2*y[x]),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (5-\sqrt {4 x^3-4 e^x+13}\right ) \\ \end{align*}